Return to Assignments Tangent line to graph

### Assignment 7

Calculate the equation of the tangent line(s) of the graph of the function:

parallel to the tangent line at the point of the graph of the function:

### Solution

First we calculate the slope of the tangent line at . For this we have to differentiate the second function:

In the point the slope is equal to:

Now we have to try and find the points on the graph of the function:

of which the tangent line(s) has (have) a slope equal to .

An tangent line at the graph of this function has a slope:

So we have to find the values of for which we have:

or:

This equation has no (real) solutions and thus the required tangent line(s) does (do) not exist. We can verify this in the figure below.

Return to Assignments Tangent line to graph