Sketching Gradient Functions


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How do we sketch the gradient function with the equation?

This is the absolute basics. If you are given the equation, you can just differentiate the equation and sketch the function.

Example 1:





How do we sketch a function without the equation?

You are more likely to get a graph without the function. It is possible to use the features of a given function to sketch the corresponding gradient function. The table below shows features of a graph of a function, y=f(x) and the graph of its gradient function, y=f'(x), at corresponding values of x:

Example 2:





Practice Question:





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Note: As this is a new part of the specification, there are not many questions to practice. The best way to practice these types of questions, is to use a graphing software like Geogebra to graph an function and then graph the derivative. But don't graph the derivative until you have drawn it yourself.