Question

Find the equation of tangent of $y=x^2$ at $x=1$

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

Answer 1

The Correct Option is A

Explanation:
Given: $y=x^2$ and $x=1$As we know that equation of tangent is $\frac{y-f(a)}{x-a}=f^{\prime }(a)$ for the function $y=f(x)$ at $x$ $=a$First find $f(a)$ and $f^{\prime }(a)$$f(1)=1$$\Rightarrow f^{\prime }(x)=2x\text{ and }{f}^{\prime }(1)=2$As we know that equation of tangent is $\frac{y-f(a)}{x-a}=f^{\prime }(a)$ for the function $y=f(x)$ at $x$ $=a$$\frac{y-1}{x-1}=2$$\Rightarrow y=2x-1$So, the equation of tangent is $y=2x-1$.Hence, the correct option is (A).