Exponential and Logarithmic Functions question

[ogg]

Hello I am having trouble with the question:
Find the equation of the horizontal line tangent to the graph of: xe^x


So far i have took the derivative to get : e^x(1+x)
I am lost what to do after this point as there is not a given point on the graph that I can sub in to find the actual number for the slope.

Any help would be great
Thanks!

 

[daon2]

Hello I am having trouble with the question:
Find the equation of the horizontal line tangent to the graph of: xe^x


So far i have took the derivative to get : e^x(1+x)
I am lost what to do after this point as there is not a given point on the graph that I can sub in to find the actual number for the slope.

Any help would be great
Thanks!

There is not a unique tangent line to this function (the only functions with this property are linear ones). You must be given at least an x-value to answer this question.

 

[MarkFL]

A horizontal line has the form:

\(\displaystyle y=k\) where k is a constant.

You have correctly differentiated, to find:

\(\displaystyle \dfrac{d}{dx}\left(xe^x \right)=(x+1)e^x\)

If we equate this derivative to zero, we find the critical value:

\(\displaystyle x=-1\)

and so the tangent line will be:

\(\displaystyle y=(-1)e^{-1}=-\dfrac{1}{e}\)

 

[daon2]

Ah I misread

 

[ogg]

A horizontal line has the form:

\(\displaystyle y=k\) where k is a constant.

You have correctly differentiated, to find:

\(\displaystyle \dfrac{d}{dx}\left(xe^x \right)=(x+1)e^x\)

If we equate this derivative to zero, we find the critical value:

\(\displaystyle x=-1\)

and so the tangent line will be:

\(\displaystyle y=(-1)e^{-1}=-\dfrac{1}{e}\)

Ah yes thank you! I forgot that if the tangent is horizontal than it is equal to zero.

Thanks!

 

[lookagain]

I forgot that if the tangent line is horizontal then > > it < < is equal to zero.

This is an incorrect use of that pronoun. What does the "it" refer to?

I forgot that if the tangent line is horizontal, then the slope there (or at that location) is equal to zero.