Math 101Exam 2 extra review problems

1. Consider the function f(x) = 120x

5 � 112x

4 + 3.

(a) Find f 0and f 00

.

(b) Find the critical points of f .

(c) Classify any local extrema.

(d) Find any inflection points.

(e) Identify the global extrema of f if the domain is restricted to [1, 2].

2. Consider the function f(x) = x5 � 10x3 � 8. Identify local extrema and points of inflection.

3. The average of two nonnegative numbers is 180. What is the largest possible product of these

two numbers?

4. Fencing costs $3 per meter and shrubbery costs $1 per meter. Suppose we want to enclose a

rectangular area which is 120 square meters in area. Two opposite sides will consist of fencing

and the other two sides will consist of shrubbery. What is the minimum cost to do this?

5. A right triangle has one leg of 7 cm. How fast is its area changing at the instant the other leg

has length 10 cm and is decreasing at 2 cm per second? Recall that the area of a triangle with

base b and height h is12bh.