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.