# What is the equation of the line normal to #f(x)= x^3-e^x # at #x=2#?

##### 1 Answer

#### Explanation:

First, we have to Find the Required Coordinate on which the Normal Line will intersect with the graph.

So, We are given that the point has

So, The required point is

Now, We need to calculate the slope of the graph on that point.

So, The equation of slope for

Now. we will just substitute

So, The slope of

Now, we know, Condition of Perpendicularity of two lines is

So, The slope of our normal line is

Now, Let's find the equation.

We know the Slope-Intercept Form of a linear equation is:

In this equation, let's substitute our slope.

So, The equation becomes,

And, This line must pass through our desired point

So, the equation must be satisfied with those values.

So, Now substituting the values of

So, We get,

Now, We will put

So, We get,

Hope this helps.