Question

Identify the point of local maxima/minima in $f\left(x\right)={(x-3)}^{10}$

• A. local maxima at $x=3$
• B. local minima at $x=3$
• C. local maxima at $x=-3$
• D. local minima at $x=-3$

Answer 1

The correct option is B local minima at $x=3$

Consider the nth derivative test.
Here $n=10$.
$f^n\left(x\right)=10\times 9\times \mathrm{8...1}$
$=10!$
Hence
$f^n>0$ and n is even.
Thus we get a minima at $x=3$