Question

Find the slope of the tangent to the curve y = x3 − 3x + 2 at the point whose x-coordinate is 3.

Answer 1

The given curve is y = x3 − 3x + 2

=$\frac{dy}{dx}$=3x2-3

The slope of the tangent to a curve at (x0, y0) is $(\frac{dy}{dx})\bigg] _{ (x_0,y_0)}$.

Hence, the slope of the tangent at the point where the x-coordinate is 3 is given by,

$(\frac{dy}{dx}) \bigg]_{x=3}$=3x2-3]x=3=3(3)2-3=27-3=24.