Question

find the slope of the curve y = - 4x^2 at (2, - 16).
the slope of the curve y = - 4x^2 at (2, - 16) is . (simplify your answer.)

Explanation:

Step1: Differentiate the function

The derivative of $y = - 4x^{2}$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ is $y'=-8x$.

Step2: Evaluate the derivative at the given x - value

Substitute $x = 2$ into $y'$. So $y'(2)=-8\times2$.

Answer:

$-16$