Question

Assertion :Equation of tangent to the curve $y=x^2+1$ at the point where slope of tangent is equal the function value of the curve is $y=2x.$ Reason: $f^{\prime }\left(x\right)=f\left(x\right)$

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

As $f^{\prime }\left(x\right)=f\left(x\right)$
$\therefore$ $2x=x^2+1$ $\Rightarrow$ $x=1$
$\therefore$ $y=2$ $\therefore$ $f^{\prime }\left(1\right)=2=m$
$\therefore$ Equation of tangent to the curve at (1, 2) is
$\Rightarrow y-2=2(x-1)$
$\Rightarrow$ $2x-y=0$

$\Rightarrow$ $y=2x$