Lesson08: Derivatives (worksheet)

Worksheet for Sections 2.6 and 2.7 Tangents, Velocity, and the Derivative Math 1a October 12, 2007 1.

Let f (x) = x3 . Use the definition of the derivative to find f 0 (2).

2.

Let f (x) =

√

x.

(a) Use the definition of the derivative to find f 0 (4).

(b) Find f 0 (x) and give its domain.

(c) Is f differentiable at zero? Use a graph to illustrate why or why not.

Here’s a useful fact: for any numbers A and B: A3 − B 3 = (A − B)(A2 + AB + B 2 ) √ 3

x = x1/3 . Use the definition of the derivative to find f 0 (x) and give its domain.

3.

Let f (x) =

4.

Repeat with f (x) = x2/3 .