Question

Assertion :If $f\left(x\right)={(x-2)}^3$ then f(x) has neither maximum nor minimum at $x=2.$ Reason: $f^{\prime }\left(x\right)=0=f^{\prime \prime }\left(x\right)$ when $x=2.$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

$\because$ $f\left(x\right)={(x-2)}^3$
$\therefore$ $f^{\prime }\left(x\right)=3{(x-2)}^2$
For maximum & minimum values $f^{\prime }\left(x\right)=0$
$\Rightarrow$ $x=2$
Now $f^{\prime \prime }\left(x\right)=6(x-2)$
$\Rightarrow$ $f^{\prime \prime }\left(2\right)=0$
$\Rightarrow$ $f\left(x\right)$ is neither maximum nor minimum at $x=2.$