Sketching Graphs
UBC Calculus Online Course Notes

## Practice with graphs

Exploring what a derivative tells us about the graph of a function

The sample questions on this page are to help you think about graphs of functions and their derivatives. If you are having problems with these types of questions, you should practice these and others like them.

1. You are given the following information about the derivative of a function f(x) for various values of x. A plus sign ("+") means that the derivative is positive, "-" means negative and "0" means the derivative is zero at that point. Determine which of the following graphs are candidates for the function.

 x -1.5 -1.1 -0.5 0 0.5 1 1.3 1.5 2 f'(x) + 0 - 0 - - 0 + +
 (a) (b) (c) (d)

Question 2:

The graph of some function is shown here. Identify which of the sign patterns for the derivative of this function that correctly matches the function.

(a)
 x -1.5 -1 -0.5 0 0.5 1 1.5 2 f'(x) + - - - - - 0 +

(b)
 x -1.5 -1 -0.5 0 0.5 1 1.5 2 f'(x) - 0 - + - 0 + +

(c)
 x -1.5 -1 -0.5 0 0.5 1 1.5 2 f'(x) - 0 + 0 - 0 + +

(d)
 x -1.5 -1 -0.5 0 0.5 1 1.5 2 f'(x) + 0 - 0 + 0 - -

Question 3:

Identify which of the graphs below might be a graph of the derivative of the function shown in the previous problem:

 (a) (b) (c) (d)

Answers: 1(b), 2(c), 3(a)