2. Graph a function which has exactly one critical point, at x = 2, and exactly one inflection point, at x = 4.In Exercises 4-8, use derivatives to find the critical points and inflection points.6. f(x = " + 15x4 + 25In Exercises 9-12, find all critical points and then use the first-derivative test to determine local maxima and minima. Check your answer by graphing.12. f (a) = 7241 In Exercises 13-16, find all critical points and then use the second-derivative test to determine local maxima and minima. 32. a. If a is a positive constant, find all critical points of f(x) = x - ax. b. Find the value of a so that fhas local extrema at x = 12.34. a. If b is a positive constant and x > 0, find all critical points of f(x) = x - b In x. b. Use the second-derivative test to determine whether the function has a local maximum or local minimum at each critical point.38. Figure 4.14 is the graph of a derivative f'. On the graph, mark the x-values that are critical points of f. At which critical points does fhave local maxima, local minima, or neither? X Figure 4.14For Problems 43-46, sketch a possible graph of y = f(x), using the given information about the derivatives y' = f'(x) and y" = f"(x). Assume that the function is defined and continuous for all real x.Answer 54. Find values of a and b so that f(x) = x2 + ax + b has a local minimum at the point (6, -5).I Problems 6263 Show graphs off, f', f". Each of these three functions is either odd or even. Decide which functions are odd and which are even. Use this information to identify which graph corresponds to which to f', and which to f". 62. I In Exercises 410, find the global maximum and minimum for the function on the closed interval. 4.f(a:) :m33m2+20, 1a:3