first derivative test Consider the function f(x) given as follows: f(x) = xe x?/8 { f(x) = x e^(-x^2/8) a) Find all the critical points of f(x). b) Apply the first derivative test to clasify each critical point as a relative maximum, a relative minimum, or neither. QUESTION 27 second derivative test Consider the function f(x) given as follows f(x) = (x- 4)2 (x+2) { f(x) = (x-4)^2 (x+2) } a. Find the first derivative and find all the critical points. b. Find the second derivative and evaluate at each critical point to classify as relative maximum or relative minimum QUESTION 28 concavity Consider the function g(x) given as follows g(x) = (x+3)2 (x- 3)2 { g(x) = (x-3)^2 (x+3)^2 } a. Find the first and second derivative g'(x) and g"(x). b. Determine where g"(x) = 0. Use this to determine the regions where g(x) is concave up and regions where concave down.