1. (a) If f(2)=2 and f(x) 5 for all x>2, then explain why f(4) 8. (b) Use the Me

ID: 2850047 • Letter: 1

Question

(a) If f(2)=2 and f(x) 5 for all x>2, then explain why f(4) 8.

(b) Use the Mean Value Theorem to demonstrate that if f(a) = b and f(x) d for all x > a, then f(x) d(x a) + b for all x a.

2. Let f(x) = 3x5 5x3. Answer the following questions. Show your calculations and give justifications or explanations.

(a) Find the critical points c of f(x) and for each such c, determine whether f(c) is a local maximum value or a local minimum value or neither.

(b) Find the intervals where f(x) is increasing and the intervals where f(x) is decreasing.

(d) Find all the points of inflection, if any, of f(x).

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