Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an answer does not exist, enter DNE.) PLEASE HELP!!!!

Question

asked Nov 25, 2023 184k views

1 Answer

Baldarn · Answer 1 · 2023-11-30T13:14:59+0000

Answer: (0, -9)

Given:

$f(x)=x^{(6)/(7)}-9$

First, we derive the given equation:

$\begin{gathered} (d)/(dx)x^{(6)/(7)}-9 \\ =\frac{6}{7x^{(1)/(7)}} \end{gathered}$

The intervals would be:

$-\inftyPlugging x=0 to f(x):[tex]\begin{gathered} f(x)=x^{(6)/(7)}-9 \\ f(0)=(0)^{(6)/(7)}-9 \\ f(0)=-9 \end{gathered}$

Therefore the relative minimum is at (0, -9)