-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
[tex]\dfrac{dy}{dx} = \dfrac{d}{dx}(x^3 -5x^2 +7) = 3x^2 -10x[/tex]
Evaluated at x = 2, the gradient of the slope is
[tex]\left.\dfrac{dy}{dx}\right|_{x=2} = 3(2)^2 - 10(2) = -8[/tex]
