14. For each of the following graphs of the function y = f(x), make a rough...

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14. For each of the following graphs of the function y = f(x), make a rough sketch of the derivative function f'(x). By comparing the graphs of f(x) and f'(x), show that the intervals for which f(x) is increasing correspond to the intervals where f'(x) is positive. Also show that the intervals where f(x) is decreasing correspond to the intervals for which f'(x) is negative. b. a. 2- y= f(x) -2 2 4 f(x) is a linear function. C. d. y= f(x) 2 20 2 y = f(x) 2- 1 2 3 f(x) is a cubic function. 2y= f(x) -20 2 -2- f(x) is a quadratic function. f(x) is a quartic function. a) 4 =4 2 +-2 4 b) -2 +-2 2 4 1 14. For each of the following graphs of the function y = f(x), make a rough sketch of the derivative function f'(x). By comparing the graphs of f(x) and f'(x), show that the intervals for which f(x) is increasing correspond to the intervals where f'(x) is positive. Also show that the intervals where f(x) is decreasing correspond to the intervals for which f'(x) is negative. b. a. 2- y= f(x) -2 2 4 f(x) is a linear function. C. d. y= f(x) 2 20 2 y = f(x) 2- 1 2 3 f(x) is a cubic function. 2y= f(x) -20 2 -2- f(x) is a quadratic function. f(x) is a quartic function. a) 4 =4 2 +-2 4 b) -2 +-2 2 4 1