Question

The function f(x) is defined as f(x) = -2(x+2)(x-1)^2 = -2(x^3 -3x + 2) on the open interval (-3,3). 1. Determine the x-coordinate of the absolute minimum of f(x) in the open interval (-3,3). Justify your answer. 2. Find all values of x for which f(x) is concave down. Justify your answer. 3. Let g(x) be defined as g(x) = abs(f'(x)), the absolute value of the derivative of f(x), in the open interval (-3,3). Determine the (x,y) coordinate of the relative maxima of g(x) in the open interval. Justify your answer. 4. Find the x-values of the relative minima of g(x)? Justify your answer.

Answer 1

are you having trouble with this? It looks like straightforward use of derivatives to find critical values and concavity. What do you get?