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

Question

Quizplus · Accepted Answer

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

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