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

##### 1 Answer

Oct 14, 2015

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