Find an equation of the tangent line to the curve at the given point. y = 2x3 − x2 + 8, (2, 20)

Question

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

y = 2x³ − x² + 8,  (2, 20)

Answer 1

Take the derivative of the function to find the slope of the tangent line for any x.

Test your point into the function to make sure the point lies on the curve. (Looks like it does to me)

Then evaluate the derivative for the x specific to the problem; I.e. Let x=2 in f’(x).

this is the slope (m) of the tangent line to the curve at the given point.

Given the slope (m) you just found, substitute it along with the point given (2,20) into y= mx+b to find the y-intercept (b). Then you have the slope (m) and intercept (b) of your tangent line so substitute them into y=mx+b for m and b and your done.