Find the equation of a tangent line to the given curve at an x-coordinate.

Question

I need to find the slope-intercept form of the tangent line that is formed when the curve of the equation y=x^3-2x-2 intersects with x=1

Answer 1

y'=slope = 3x^2 -2x = 3(1)^2 -2(1) =3-2 = 1

y=(1)x + b, x=1, y= 1^3 -2(1) - 2 = -3

-3 =1 +b

b = -4

tangent line is y=x-4 at x=1