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

Question

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the derivative of the function and evaluate it at the given point.

$$\frac{dy}{dx} = 1 - 2x$$

When x = 2, $$\frac{dy}{dx}$$ = -3

So the equation of the tangent line is:

\begin{align*}
y - y_1 &= m(x - x_1)\
y - (-2) &= (-3)(x - 2)\
y &= -3x + 4
\end{align*}

Therefore, the answer is A.

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