Question

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

Answer 1

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)