Calculus I-Review Problems for Exam 2

1. Find the equation of the line tangent to f(x) at x = 2, if

2. Suppose f and g are differentiable functions with the values shown in the following table. For each of the following functions h, find h' (2).

3. If f is a differentiable function, find an expression for the derivative of each of the following functions:

4. Given y = f(x) with f(1) = 4 and f 0 (1) = 3, find

5. Differentiate the following functions.

(a) y = 2 sec x − csc x

(b) y = 2−tan x/x

(c) y = tan x/1− sec x

(d) y = x2 sin x tan x

6. Let y 2 + 4x = 4xy2 .

(a) Find dx/dy.

(b) Find the equation of the tangent line to this curve at (1/3, 2)

(c) Find the x- and y-coordinates of all points at which the tangent line to this curve is vertical.

7. In the following problems find the local lincarization of f(z) near z = 0 and use this to approximate the value of a.

8. Use a linear approximation to estimate the given number.

9. Consider the piecewise linear function defined below.

For each function g(x), find the value of g' (3).