Find the absolute maximum and minimum values of the function over the indicated

Question

Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur. f(x) = (x + 5)^2/3 -2; [-7,6] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The absolute maximum value is Q at x = (Type integers or decimals rounded to two decimal places as needed. Use a comma to separate answers as needed.) There is no absolute maximum value. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The absolute minimum value is Q at x = (Type integers or decimals rounded to two decimal places as needed. Use a comma to separate answers as needed.) There is no absolute minimum value.

Explanation / Answer

There is no absolute maximum value the function is a decreasing one between [-7,-5] and increasing in [-5,6]

Absolute minima occurs at x=-5

It is evident from the fact that (x+5)^{2/3} is a positive quantity and minimum is -2 when the term is 0.

(x+5)^{2/3} becomes zero only at x=-5

Hence it has an absolute minimum occuring at x=-5

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