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.