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Derivative of a Linear Function

What does the derivative look like?

Without checking the Derivative checkbox above see if you can determine the shape of the graph of the derivative. Check your solution by clicking on the checkbox for Derivative above. Manipulate the sliders or input boxes to change the values of m and b to get different linear functions.

Geometric Proof

The graph of a linear function (first degree polynomial function) is a straight line. At any point the secant and tangent lines to the graph are all identical with the original graph. The slopes of the original line, secant lines, and tangent lines are all equal to the coefficient of the x term. For the formal algebraic proof using the definition of the derivative, click on the proof checkbox above.