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