Find an equation of the tangent line to the curve at the given point.

Question

Find an equation of the tangent line to the curve at the given point.

y = X^3 - 2x + 2, (3,23)

y =

Answer 1

y= x^3 -2x +2

y' = 3x^2 -2

y'(3) = 3(3^2)-2 = 25 = slope of the tangent line at x=3

y=25x +b

23=25(3)+b

b =23-75=-52

y=25x - 72 is the tangent line's equation at the given point (3,23)