Find the relative maxima, and use a graphing utility to check your results. Round your answer to two decimal places.

Question

Find the relative maxima, and use a graphing utility to check your results. ​Round your answer to two decimal places. ​  ​

Quizplus · Accepted Answer

To find the relative maxima, we need to find the critical points where the derivative is 0 or undefined. Taking the derivative of the function and setting it equal to 0, we get:
f'(x) = 3x^2 - 8x = x(3x - 8)
Setting x = 0 or 3/8, we get the critical points. We then need to check the value of the function at these points and the endpoints of the interval [-1,2]. 
f(-1) = 15, f(0) = 10, f(2) = -10/3, f(3/8) = 49/16
The relative maxima occur at x = 0 and x = 3/8 where the function takes the values 10 and 49/16, respectively. Using a graphing utility, we can visualize the function and confirm that the points (0,10) and (0.375, 3.06) are relative maxima.

Find the Relative Maxima, and Use a Graphing Utility to Check