Question

The function f given by f(x) =9x^(2/3) +3x-6 has a relative minimum at x=?

Answer 1

when f'(x)=0
f''(x)>0

Answer 2

\[\Large{6 \over \sqrt[3]{x}}+3=0\]

Answer 3

Differentiate the function w.r.t. x
\[6x ^{-4/3}+3\]
From which is obtained:
\[\sqrt[3]{x}=-2\]
x = -8

Answer 4

When the result of differentiation is put equal to zero.

Answer 5

Take derivative of the function and then set it equal to zero to get critical points. Then use the either first or second derivative test to find the desired local extrema