Question

Find the extreme values of the function and where they occur. f(x)=x-4sqrt(x)

Answer 1

The extreme values of the function f(x) = x - 4sqrt(x) occur at the values of x for which f'(x) = 0

f'(x) = 1 - 2/sqrt(x) = 0
sqrt(x) - 2 = 0
sqrt(x) = 2
x = 4
To check for minimum or maximum,
f''(x) = 1/(sqrt(x))^3 = 1/(sqrt(4))^3 = 1/(2^3) = 1/8 => the point is a minimum.

Therefore, the minimum value = f(4) = 4 - 4sqrt(4) = 4 - 4(2) = 4 - 8 = -4 and occurs at x = 4.