Question

Assertion :If $f\left(x\right)=max.(x^2-4x+6,|x-2|)$,the greatest value of $f\left(x\right)$ in the interval $[0,5]$ is $11$ Reason: The largest value of $f\left(5\right)=max.(11,3)=11$

• 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

$\because$ $f\left(x\right)=max.\{{(x-2)}^2+2,|x-2|\}$
$\Rightarrow$ $f\left(x\right)={(x-2)}^2+2$ $\Rightarrow$ $f^{\prime }\left(x\right)=2(x-2)$
$\therefore$ $f^{\prime }\left(x\right)=0$ $\Rightarrow$ $x=2ϵ[0,5]$
$\therefore$ Greatest value of $f\left(x\right)=max.\left(f\right(0),f(2),f(5\left)\right)=max.(6,2,11)=11$
Hence Assertion is correct and Reason is also correct but it it not correct explanation of Assertion.