Question

Find the gradient of the curve y=-x^-3-5x^2+7x at x=2​

Answer 1

-8

Step-by-step explanation:

The gradient or slope of a curve y is simply the derivative of the curve at a point x. So we can proceed as follows

$\dfrac{dy}{dx} = \dfrac{d}{dx}(x^3 -5x^2 +7) = 3x^2 -10x$

Evaluated at x = 2, the gradient of the slope is

$\left.\dfrac{dy}{dx}\right|_{x=2} = 3(2)^2 - 10(2) = -8$