Find the minimum and maximum values of fx 3 Squareroot x2 o

Find the minimum and maximum values of f(x) = 3 Squareroot x^2 on the interval [-4, 7] The minimum value is _______. The maximum value is _______.

Solution

f(x) = x^2/3 on interval [-4,7]

f\'(x) = 2/(3x^1/3)

f\'(x)= 0 , => no critical points.

Checking on interval given:

f(7) = (7)^2/3  - (maximum value)

And y cannot be negative .So , in given interval minimum value , at x=0 f(0) = 0

Minimum value = 0  , Maximum value = 7^2/3

Minimum value does not exist in given interval