Question

A) Find the equation of the tangent line to the curve y = 5e^-8x at the point (0, 5).

B) Solve for t.

e^0.09t = 9

C) Rancher Johann wants to build a three-sided rectangular fence near a river, using 280 yards of fencing. Assume that the river runs straight and that Johann need not fence in the side next to the river.

Johann wants to build a fence so that the enclosed area is maximized.

• What should be the length of each side running perpendicular to the river?
  yards
  
• What should be the length of the side running parallel to the river?
  yards
  
• What is the largest total area that can be enclosed?
  square yards

D) Find the absolute maximum and minimum values on the closed interval [-3,3] for the function below. If a maximum or minimum value does not exist, enter NONE.

f(x) = (4x)/(x² + 1)

E) When a baseball park owner charges $5.00 for admission, there is an average attendance of 100 people. For every $0.25 increase in the admission price, there is a loss of 2 customers from the average number.

1. What admission price should be charged in order to maximize revenue
   
2. What is the maximum revenue?

F) Find the derivative.

f(x) = x⁶ · e^2x

Answer 1