Find an equation of the tangent line to the curve 𝑦 = x^3 − 2𝑥 at the point (2, 4)

Answer 1

Hello!

In order to properly define a line (using point slope form), it suffices to compute the slope of the line, as a point was already given to us. In calculus, whenever we hear "slope," we should immediately think derivative, and calculate:

y' = 3x² -2 which, evaluated at x = 2, gives y'(2) = 10

Plugging this into our point slope form, we have

y - 4 = 10 (x - 2)

If you plug this into a graphing software, you will be able to check that this answer lines up with what we expect.