Q.For the curve $y = x^{3} - 2x$, find the slope of the tangent at $x = 2$.

The slope of the tangent is the derivative evaluated at the point. …

The slope of the tangent at a point is the value of $\dfrac{dy}{dx}$ there.

Differentiate: $\dfrac{dy}{dx}=\dfrac{d}{dx}(x^3-2x)=3x^2-2$.

Evaluate at $x=2$:

$\left.\frac{dy}{dx}\right|_{x=2}=3(2)^2-2=3\cdot4-2=12-2=10.$ …

Differentiate first, then substitute $x=2$ — do not substitute $x=2$ into $y$ (that gives …