#### Answer

$f'(x)=10$

#### Work Step by Step

To find the slope of a function at any given point, all one has to do would be to look for the value of the derivative function at the same x value.
Given that $f(x)=x^3-2x+7$, then the derivative function by the power rule will be $f'(x)=3x^{3-1}-2x^{1-1}+7=3x^2-2$
As such, the slope at the point $x=-2$ would be $f'(-2)=3(-2)^2-2=10$