Sketch the graph of a function that satisfies all of the given conditions. f(0) = f'(2) = f'(4) = 0 f(x) > 0 if x <0 or

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Sketch The Graph Of A Function That Satisfies All Of The Given Conditions F 0 F 2 F 4 0 F X 0 If X 0 Or 1 (42.32 KiB) Viewed 12 times

Sketch the graph of a function that satisfies all of the given conditions. f(0) = f'(2) = f'(4) = 0 f(x) > 0 if x <0 or 2 < x < 4 f'(x) < 0 if 0 < x < 2 orx > 4 f"(x) > 0 if 1<x<3, f"(x) < 0 if x < 1, x > 3 For the function f(x) = x³ - 12x + 2, a. Find the intervals of increase of decrease. b. Find the local maximum and minimums values, and where they occur. c. Find the intervals of concavity and the inflection points. d. Use the information from part a)-c) to sketch the graph. Be sure to completely label your graph. Check your work with a graphing device if you have one. Suppose the derivative of a function f is f'(x) = (x + 1)²(x-3) 5 (x-6)4. On what interval is f increasing? Let f(t) be the temperature at time t where you live and suppose that at time t = 3 you feel uncomfortably hot. Which of the following would be the best case scenario? Which would be the worst? Explain your reasoning. a. f(3) = 2,f"(3) = 4 b. f(3) = -2,f"(3) = 4 c. f'(3) = 2,f"(3) = -4 d. f'(3) = -2,f"(3) = -4 Find a cubic function f(x) = ax³ + bx² + cx + d that has a local maximum value of 3 at x = -2 and a ocal minimum value of 0 at x = 1.