Question

The equation of tangent to the curve $y=x^2-1$ at $x=1$ is

• A. $y=2x-2$
• B. $y=2x+2$
• C. $y=2x+1$
• D. $y=2x-1$

Answer 1

The correct option is A $y=2x-2$

Given curve, $y=x^2-1$
At $x=1\Rightarrow y=0$
Now, slope of tangent at $x=1$ is
$f^{\prime }\left(1\right)=\underset{h\to 0}{lim}\frac{f(1+h)-f\left(1\right)}{(1+h)-1}$
$\Rightarrow f^{\prime }\left(1\right)=\underset{h\to 0}{lim}\frac{(1+h{)}^2-1-0}{1+h-1}$
$\Rightarrow f^{\prime }\left(1\right)=\underset{h\to 0}{lim}\frac{h^2+2h}{h}$
$\Rightarrow f^{\prime }\left(1\right)=\underset{h\to 0}{lim}(h+2)$
$\Rightarrow f^{\prime }\left(1\right)=2$
$\therefore$ Equation of tangent is
$\Rightarrow y-0=2(x-1)$
$\therefore y=2x-2$