Question

Find the equation of the tangent to the curve $y=x^2+1$ at the point $(1,2)$.

Answer 1

$A]y=x^2+1$

Differentiating,

$y^1=2x$

$y^{1}at(1,2)=2\left(1\right)=2$

using slope - point form

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

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

y - 2 = 2x - 2

$\therefore$ y = 2x [equation of tangent]