need help with the following with explanations, thank you

Word Document15 v PR Accessibility Mode ) Immersive Reader Edit Print 15 Share Page 179: problems 2, 8, 10, 12, 18, 20, 22, 24, 26, 30, 39, 40, 41, 42, 44 In Problem 2, indicate all critical points of the function f. How many critical points are there? Identify each critical point as a local maximum, a local minimum, or neither. S(x) A In Problems 8,10,12 (a) Use the derivative to find all critical points. (b) Use a graph to classify each critical point as a local minimum, a local maximum, or neither. 8. f(x) = 5x - x42+8 10. f(x) = 9x^2 -x^3 12. f(x) = x^4 - 4x^3 In Problem 18, graph the function and describe in words the interesting features of the graph, including the location of the critical points and where the function is monotonic (that is, increasing or decreasing). Then use the derivative and algebra to explain the shape of the graph. 18. f(x) = x In x, x>0 In Problem 20, find the critical points of the function and classify them as local maxima or minima or neither. 20. g(x) = xe^-3x In Problems 22,24, find all critical points and then use the first-derivative test to determine local maxima and minima. Check your answer by graphing- 22. f(x) = 3x^4 - (4x*3) + 6 24. f(x) = (x*3 - 8)^4 " In Problem 26, the continuous function has a critical point. (a) Is the critical point a local maximum or a local minimum? (b) Sketch the graph near the critical point. Label the coordinates of the critical point. 26. f(1) = 5, f '(1) = 0, f "(1) =-2 30. The function f(x) = x^4 - 4x^3 + 8x has a critical point at x = 1. Use the second-derivative test to identify it as a local maximum or local minimum. " In Problems 39,40,41 the function f is defined for all x. Use the graph of f ' to decide: Page 1 of 2 75% Give Feedback to Microsoft