Question

How do you find the equation of the tangent to the curve `y=x^3-6x` at (2,-4)?

Answer 1

Differentiate.
Replace x value, find the gradient.
Using y=mx+c, replace the value of c and get the equation.
(y=6x-22)

Explanation:

So differentiating x^3-6x i.e dy/dx
So,

dy/dx=3x^2-6.
This is equal to the gradient of the tangent.
3x^2-6=m, x=2

3*4-6=m
m=6.

Now, y=mx+c

-4=6*3+c
-4=18+c
-4-18=c
c=-22

Equation of tangent=> y=6x-22