Find an equation for the tangent to the curve at the given point.
-$$y = x ^ { 2 } - 1 , ( 2,3 )$$
A) $y = 4 x - 9$
B) $y = 4 x - 5$
C) $y = 2 x - 5$
D) $y = 4 x - 10$

Question

Quizplus · Accepted Answer

The derivative of $y = x^2 - 1$ is $y' = 2x$. At $x = 2$, the slope is $2(2) = 4$. Using the point-slope form $y - y_1 = m(x - x_1)$ with point $(2,3)$, the equation is $y - 3 = 4(x - 2)$, which simplifies to $y = 4x - 5$.

Find an Equation for the Tangent to the Curve at the Given