Question

Find the extreme values of each function on the interval!! 10 points!!?

³√(x) ; -2 ≤ x ≤ 27

answer:

C) max= (27,3) and min = (0,0)

This is the last problem I have and I cannot figure out how to get this answer! Can someone show me please??? Thanks in advance!!

Answer 1

Sorry the question says "find the ABSOLUTE extreme values of each function on the interval"

Answer 2

f(x) = ³√(x)
f'(x) = 1/3x^(-2/3) = 1/(3x^2/3)
which is positive for all values of x and is 0 at x = 0.
Therefore, f(x) is an increasing function. In any interval, it will attain its maximum at the right endpoint of that interval because the function always increases as x increases.

Answer 3

In the interval [-2,27], f(x) will attain its maximum when x = 27
f(27) = (27)^(1/3) = 3. The max point is (27,3).

When x = 0, f(x) = 0.
When we take the absolute value, all the negative f(x) will become positive and the lowest or the minimum will be 0. Therefore, absolute minimum occurs at x = 0 and the point is (0,0).