Question

Find equation of tangent for curve $y=x^2$ at (1,1)

• A. y=2x-1
• B. y=2x
• C. y=x+1
• D. None of these

Answer 1

The correct option is A y=2x-1

The given equation of curve is,

$y=x^2$

Thus, slope of tangent to the curve is given by,

$m=\frac{dy}{dx}$

$\therefore m=\frac{d\left(x^2\right)}{dx}$

$\therefore m=2x$

Slope of tangent at point $(1,1)$ is,

$m=2\times 1$

$\therefore m=2$

Thus, equation of tangent at point $(1,1)$ is given by two point form as,

$y-y_1=m(x-x_1)$

$y-1=2(x-1)$

$\therefore y-1=2x-2$

$\therefore 2x-y-1=0$

$\therefore y=2x-1$

Thus, answer is option (A)