Derivative Graph of a Function
Learning Objective: Given a function's graph, sketch the graph of its derivative.
Class Opening: We will discuss graphing the derivative of this piecewise function.
Directions: Use the graph below for all questions that need you to graph a function. Enter a function and hit return. Use the slider to view the graph of it's derivative or the slope of a line tangent to the curve at an x-value. The green line is the function and the red line is the derivative of that function.
Graph the following linear functions and view their derivatives by moving the slider.
, ,
What similarities did you notice in the graphs of the three linear functions?
Given the graphs below, sketch the derivatives of both on the same graph. Check your answers using and
Now, graph the following quadratic functions or parabolas. And look at their derivatives.
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How do you know when the derivative will cross the x-axis? (Hint: look at the slope of the tangent line at that point)
How do you know when the derivative will be above the x-axis? Below the x-axis?
Using the parabola below, sketch what you think the derivative will be. Check your answer with the graph above and the equation
Using the parabola below, sketch what you think the derivative will be. Check your answer with the graph above and the equation
Challenge: using the graph below sketch what you think the derivative will be.