WeBWork 4 - Topics 8 - 9: Problem 5 (1 point) Consider the function f(ac) - -2ac2 + 8ac - 3. Find the critical point, A, of the function. A At a = A, does f (a) have a local min, a local max, or neither? Type in your answer as LMIN, LMAX, or NEITHER . Answer Note: You can earn partial credit on this problem.WeBWork 4 - Topics 8 - 9: Problem 2 (1 point) Consider the function f(x) = xe -8x, 0Xx52. This function has an absolute minimum value equal to: which is attained at x = 1 and an absolute maximum value equal to: which is attained at x = Note: You can earn partial credit on this problem.WeBWork 4 - Topics 8 - 9: Problem 8 (1 point) You are given the following graph of the function f(x): 50 -10 Find the point where the second derivative changes sign from negative to positive? X=WeBWork 4 - Topics 8 - 9: Problem 9 (1 point) 1 0 Identify the graphs A (blue), B(red) and C (green) as the graphs of a function f() and its derivatives f'(a) and f" (x). (Clicking on the sketch will give you a version of the picture in a separate window.) is the graph of the function, f(a). ? is the graph of the function's first derivative, f'(a) . ? is the graph of the function's second derivative, f"(x) Hint: Remember that f'(a) is itself a function, and we can find the derivative of the function f'(2), which is called the second derivative of the function f (x) and denoted by f" (x).WeBWork 4 - Topics 8 - 9: Problem 4 (1 point) A rectangular storage container with an open top is to have a volume of 100m . The length of its base is twice the width. Material for the base costs $12 per square meter. Material for the sides costs $20 per square meter. Find the dimensions and the cost of materials for the cheapest such container. . Width: m . Length: m . Height: m . Cost: $ Note: You can earn partial credit on this problem.WeBWork 4 - Topics 8 - 9: Problem 3 (1 point) Find two numbers differing by 50 whose product is as small as possible. Enter your two numbers as a comma separated list, e.g. 2, 3. The two numbers areWeBWork 4 - Topics 8 - 9: Problem 6 (1 point) f(2) = 2 + 4.5x2 - 12x - 2 a) Find f'(a). b) Identify the graph that displays f in blue and f'in red. ? v B. c) Using the graphs of f and f , indicate where f is increasing and decreasing. Give your answer in the form of an OPEN interval. NOTE: When using interval notation in WeBWork, remember that: You use 'INF' for oo and '-INF' for - co. And use 'U' for the union symbol. Enter DNE if an answer does not exist. f is increasing on f is decreasing onWeBWork 4 - Topics 8 - 9: Problem 7 (1 point) Suppose that on the interval I, f(x) is positive and concave up. Furthermore, assume that f"(x) exists and let g(x) = (f(x) )2. Use this information to answer the following questions. To answer the questions, choose your answers from the following list: CU (concave up), CD (concave down), f(x) , f(x) , f(x) , 0, or 1. a.) f" (z ) > on I . b.) g" (x) = 2(A2 + Bf"(z)), where A = and B = c.) g"(x) > on I. d.) g(a) is on I. ote: You can earn partial credit on this