# What is the equation of the line normal to # f(x)=lnx-x^3# at # x=1#?

##### 1 Answer

Jan 15, 2016

#### Explanation:

First find the gradient of

The rest of the equation can be found by substituting in the values at the given point.

At

Therefore the slope of the normal is

Going back to the original expression

f(1) = ln(1) - 1^3 = 0 -1 = -1#

The equation of the normal is

At the given point

The equation of the normal is

or