1) If f'(t) = 9t^2 + e^t and f(0) = 4. Compute f(3)

2) The velocity of a car at time t seconds is given by v(t)=6t +(3/64)t^2 feet per second. How far does the car travel from t=0 to t=4?

3) You drop a stone off a cliff. Its initial height is 500500 feet. Its velocity at time t seconds is 32t feet per second. What is the height of the stone after 3 seconds?

4) Find k so that x^7e^(x^8)dx = ke^(x^8)+C

5) Your marketing department estimates that if you sell x units of your product, then your marginal profit is P'(x)=900+1.8x (recall that marginal profit is the derivative of profit). Because of start-up costs, P(0)=9000. Find a formula for P(x) the profit if you sell x units.