Answer: (0, -9)
Given:
[tex]f(x)=x^{\frac{6}{7}}-9[/tex]
First, we derive the given equation:
[tex]\begin{gathered} \frac{d}{dx}x^{\frac{6}{7}}-9 \\ =\frac{6}{7x^{\frac{1}{7}}} \end{gathered}[/tex]
The intervals would be:
[tex]-\inftyPlugging x=0 to f(x):[tex]\begin{gathered} f(x)=x^{\frac{6}{7}}-9 \\ f(0)=(0)^{\frac{6}{7}}-9 \\ f(0)=-9 \end{gathered}[/tex]
Therefore the relative minimum is at (0, -9)
