Practice with derivatives

Erin Horst

For the following practice with derivatives problems, you need not use derivative formulas. By understanding the concept of derivative, you have the skills to complete all the following problems.


1.) Match the following five functions (a-e) with their respective derivative (i-v). Note: you need not know the differentiation rules to find the respective derivative.

a.) b.)

c.) d.)



(i) (ii)

(iii) (iv)



2.) Consider the graph of a function f.

a) What is the domain of f?

b) At which values of x is f not differentiable?

c) What is the domain of f'?


3.) Let h(x)=f(g(x)), where f and g have the graphs given below:

a) Evaluate h(-1) and h(2).

b) Is h'(1) positive, negative, or zero? Explain how you know this.

c) Is h'(0) positive, negative, or zerio? Explain how you know this.


4.) To test your understanding further, the graphs of two functions f and g are given below, what is the derivative of h(x)=f(x)-g(x)?




These problems were adapted from a Math Excel course taught at Portland State University, spring term 2004 by Joe Ediger and Erin Horst.