7 questions

21 minutes

See All test questions

Calculator Allowed

1. Find two non-negative numbers x and y whose sum is 100 and for which x^{2}y is a maximum.

2. Find the distance traveled (to three decimal places) from t = 1 to t = 5 seconds, for a particle whose velocity is given by v(t) = t + ln t.

3.

4. The volume of a cube is increasing at a rate proportional to its volume at any time t. If the volume is 8 ft^{3} originally, and 12 ft^{3} after 5 seconds, what is its volume at t = 12 seconds?

5. If f(x) = , find f″(40).

6. A particle's height at a time t ≥ 0 is given by h(t) = 100t - 16t^{2}. What is its maximum height?

7. If f(x) is continuous and differentiable and , then b =