Find the absolute maximum and minimum values of the following function on the gi

Question

Find the absolute maximum and minimum values of the following function on the given interval. Then graph the function. Identify the points on t graph where the absolute extrema occur. g(x) = 3x3 e-x-1sxs6 Find the absolute maximum. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ? A. The absolute maximum value occurs at x- O B. There is no absolute maximum. Find the absolute minimum. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ( A. The absolute minimum value occurs at x = O B. There is no absolute minimum. 0. (Use a comma to separate answers as needed. Round to three decimal places as needed.) (Use a comma to separate answers as needed. Round to three decimal places as needed.)

Explanation / Answer

g(x) = 3x3e-x

g'(x) = 9x2e-x+ 3x3e-x

g'(x) = 0

9x2e-x- 3x3e-x=0

3x2e-x(3 - x)=0

x=0 , x=3

g(-1) =-3 e1=-8.155, g(0)=0,g(3) = 4.033,g(6) = 3(6)3e-6 =1.584

S0 absolute maximum is (3,4.033) and minimum is (-1, -8.155)

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