22M:031 – FINAL EXAM

1. Find the derivative of F(x) = dt

2. Compute the derivative , if y = . Do not simplify.

3. Find the absolute maximum and minimum values of y = x³(x + 1) on the closed interval [–2,3].

4. Find the derivative of y = ln(e^2x).

5. Compute the antiderivative dx .

6. Find the volume of the solid obtained by rotating the graph of y = 2, for x from 1 to 4, about the x-axis.

7. Find the area of the region between the two curves y = x², and y = 4x – 3.

8. Determine where the function f(x) = is increasing or decreasing.

9. Compute the indefinite integral dx .

10. The strength of a wooden beam of fixed length is directly proportional to the product of the square of its height, h, and the width, w. That is,

S = kh2w

where k is a constant. Find the dimensions of the strongest beam which can be cut from a log with a round cross-section of radius 6 inches.

11. Find the definite integral dx.

12. State the definition of the derivative of y = f(x) (in terms of a limit of a difference quotient).