Question

A function f such that $f^{{}^{\prime }}\left(2\right)=f^{\prime \prime }\left(2\right)=0$ and f has a local maximum of - 17 at x = 2 is :

• A. ${(x-2)}^4$
• B. $3-{(x-2)}^4$
• C. $-17-{(x-2)}^4$
• D. None of these

Answer 1

The correct option is C $-17-{(x-2)}^4$

$f\left(x\right)=-(x-2{)}^4-17$

$\Rightarrow f\text{'}\left(x\right)=-4(x-2{)}^3$

$\Rightarrow f\text{'}\text{'}\left(x\right)=-12(x-2{)}^2$

Which satisfies

$f\text{'}\left(2\right)=f\text{'}\text{'}\left(2\right)=0$

and also it has a local maxima i.e.

$f\left(2\right)=-17$