Question

Find the slope of the tangent to the curve y = x 3 − 3x + 2 at the point whose x-coordinate is 3.

Answer 1

we know, slope of tangent = value of 1st derivative of curve.
in mathematically, if f(x) is function.
then, slope of tangent of f(x) at (x = a)= $\frac{dy}{dx}|_{x=a}$

here, f(x) = x³ - 3x + 2
differentiate f(x) with respect to x
$\frac{df(x)}{dx}|_{x=3}=3x^2-3\\\\\frac{df(x)}{dx}|_{x=3}=3(3)^2-3=27-3=24$

hence, slope of tangent = 24