GeoGebra

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1

What Are GeoGebra Views?

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How to Do Basic Math in GeoGebra

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The Keyboard Shortcuts and Settings of GeoGebra

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How to Use the CAS Calculator in GeoGebra

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How to Use the Spreadsheet View in GeoGebra

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How to Insert GeoGebra content in an Exam Answer File

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How to Do Sequences in GeoGebra

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Use the Sum Command in GeoGebra for Sums and Series

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How to Find Prime Numbers with GeoGebra

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Find the Scientific Notation of a Number Using GeoGebra

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How to Calculate Percent and Growth Factors in GeoGebra

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How to Use Prefixes in GeoGebra

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GeoGebra Template for Calculating Your Monthly Paycheck

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Spreadsheets for Budget and Accounting in GeoGebra

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Revenue, Cost, Unit Cost and Profit in GeoGebra

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Revenue with Demand and Price in GeoGebra

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How to Calculate Marginal Revenue with GeoGebra

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How to Find Cost-minimizing Input with GeoGebra

Use GeoGebra to find the optimum level of production that minimizes the production costs of a business.

GeoGebra Instruction 1

1.: Open Algebra View and Graphics View under View in Menu.
2.: Enter the cost function in Algebra View by typing C = <cost function> and pressing Enter.
3.: Enter the unit cost function in Algebra View by typing U = Expand(C/x) and pressing Enter.
4.: Enter C’ in Algebra View and press Enter.
5.: To view only $C^{'} (x)$ and $U (x)$ in Graphics View, tap the dot in front of $C (x)$ . The graph of $C (x)$ is hidden when it is unchecked.
6.: In order to find the points of intersection between $U (x)$ and $C^{'} (x)$ , press Intersect in Toolbar and then click on the graphs of $U (x)$ and $C^{'} (x)$ .
7.: The $x$ -coordinate of the intersection point $A$ is the cost-optimal production level.

Screenshot of GeoGebra showing the intersection of U(x) and C’(x)

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How to Find Profit-maximizing Input with GeoGebra

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How to Graph a Vector in GeoGebra

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How to Graph a Position Vector in GeoGebra

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How to Graph Vector Sums and Differences in GeoGebra

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How to Check If Two Vectors are Parallel Using GeoGebra

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How to Graph a Vector of Given Length in GeoGebra

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How to Compute Scalar Products of Vectors with GeoGebra

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Parametrization of Curves with GeoGebra

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How to Solve Vector Equations with GeoGebra

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Position, Velocity, Speed and Acceleration in GeoGebra

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How to Compute Vector Products with GeoGebra

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How to Make Lines and Planes in GeoGebra

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Find Angles Between Objects in Space with GeoGebra

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How to Find Distance in GeoGebra

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How to Make a Sphere in GeoGebra

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How to Find Intersection in GeoGebra

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Completing the Square Using GeoGebra

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How to Solve an Equation in GeoGebra

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How to Solve Systems of Equations in GeoGebra

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Solve Multivariate Systems of Equations in GeoGebra

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How to Solve Inequalities in GeoGebra

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How to Compute Logarithms in GeoGebra

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Figures, Perimeter (Circumference) and Area in GeoGebra

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How to Draw Loci with GeoGebra

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Check If Two Figures are Congruent Using GeoGebra

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How to Find Circumcircle and Circumcenter with GeoGebra

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How to Find Incircle and Incenter Using GeoGebra

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How to Find Centroid and Medians with GeoGebra

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How to Find Orthocenter and Altitudes with GeoGebra

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How to Find the Euler Line of a Triangle in GeoGebra

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How to Make a Circle in GeoGebra

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How to Graph Circles of Apollonius in GeoGebra

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How to Study the Power of a Point Theorem with GeoGebra

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How to Graph an Ellipse in GeoGebra

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Translation of Figures in GeoGebra

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Constructing Parallels in GeoGebra

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Constructing a Parallel through a Point in GeoGebra

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How to Do a Reflection in GeoGebra

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Constructing the Tangents to a Circle in GeoGebra

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How to Create an Angle in GeoGebra

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How to Construct Supplementary Angles in GeoGebra

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How to Check if Two Angles are Equal with GeoGebra

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Inscribed and Central Angles in GeoGebra

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How to Rotate a Figure in GeoGebra

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Constructing the Normal Through a Point in GeoGebra

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How to Construct a Perpendicular Bisector in GeoGebra

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How to Construct an Angle Bisector in GeoGebra

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How to Make a Polyhedron in GeoGebra

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How to Draw Prisms in GeoGebra

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How to Draw Cylinders in GeoGebra

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How to Make Pyramids in GeoGebra

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How to Make a Cone in GeoGebra

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How to Make a Sphere in GeoGebra

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Surface Area and Volume of Solid Figures in GeoGebra

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How to Make a Unit Circle in GeoGebra

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How to Use Trigonometric Functions in GeoGebra

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Calculate with the Law of Sines and Cosines in GeoGebra

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How to Solve Trigonometric Equations in GeoGebra

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How to Graph a Trigonometric Function in GeoGebra

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Transforming into a Harmonic Oscillator in GeoGebra

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Perspective Drawing in GeoGebra

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How to Make a Frequency Table with GeoGebra

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How to Make a Bar Chart with GeoGebra

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How to Make a Pie Chart with GeoGebra

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How to Make a Line Chart with GeoGebra

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How to Make a Box Plot with GeoGebra

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How to Make a Histogram with GeoGebra

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How to Calculate Central Tendencies with GeoGebra

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Relative Frequency and Law of Large Numbers in GeoGebra

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Compute Permutations and Combinations in GeoGebra

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How to Use GeoGebra as Binomial Distribution Calculator

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Hypergeometric Distribution Calculator in GeoGebra

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How to Use GeoGebra as a Normal Distribution Calculator

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Hypothesis Testing of Binomial Distribution in GeoGebra

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Hypothesis Testing with Normal Distribution in GeoGebra

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How to Graph a Function in GeoGebra

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How to Find Domain and Range of a Function in GeoGebra

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How to Find Intersection with the Axes in GeoGebra

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How to Find Intersection Between Graphs in GeoGebra

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How to Find the Zeros of a Function in GeoGebra

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How to Show Asymptotes in GeoGebra

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How to Draw a Tangent to a Curve in GeoGebra

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How to Animate Instantaneous Rate of Change in GeoGebra

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How to Calculate Limits of Functions Using GeoGebra

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How to Find the Derivative of a Function in GeoGebra

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How to Find Stationary Points in GeoGebra

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How to Find Inflection Points in GeoGebra

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How to Use Integral in GeoGebra

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How to Find the Area Under a Graph Using GeoGebra

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How to Find the Area Between Graphs Using GeoGebra

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How to Find Solid of Revolution in GeoGebra

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Integral Curves and Direction Fields in GeoGebra

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How to Write a Differential Equation in GeoGebra

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How to Do Regression in GeoGebra

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How to Solve Linear Optimization Problems with GeoGebra