# Identifying any cusp or vertical tangents

• Jun 6th 2010, 04:40 AM
dkssudgktpdy
Identifying any cusp or vertical tangents
I am not sure how to identify any cusp or vertical tangents. I can find the coordinates of the local extrema using the interval charts, though.

Can somebody help me with these following question:

Q. Determine the ecoordinates of the local extrema. Identify any cusps or vertical tangents.
a) y=-t^(2)e^(3t)
b) y= (x-5)^(1/3)
c) f(x)=(x^(2)-1)^(1/3)
• Jun 6th 2010, 05:45 AM
oldguynewstudent
Quote:

Originally Posted by dkssudgktpdy
I am not sure how to identify any cusp or vertical tangents. I can find the coordinates of the local extrema using the interval charts, though.

Can somebody help me with these following question:

Q. Determine the ecoordinates of the local extrema. Identify any cusps or vertical tangents.
a) y=-t^(2)e^(3t)
b) y= (x-5)^(1/3)
c) f(x)=(x^(2)-1)^(1/3)

Minima and maxima occur when the derivative is zero, also vertical tangeants when the derivative doesn't exist. (I think I remembered that last part right)

so dy/dt = \$\displaystyle 2t*e^{3t} + t^2 3e^{3t}\$; solving for zero gives t=-2/3. I think t=0 is also an extrema point but I'll leave that to you to check out. Also check your answer using a graphing calculator or software such as MATLAB. If you need further help, please ask and I'll detail the answer further.
• Jun 6th 2010, 07:00 AM
dkssudgktpdy
Quote:

Originally Posted by oldguynewstudent
Minima and maxima occur when the derivative is zero, also vertical tangeants when the derivative doesn't exist. (I think I remembered that last part right)

so dy/dt = \$\displaystyle 2t*e^{3t} + t^2 3e^{3t}\$; solving for zero gives t=-2/3. I think t=0 is also an extrema point but I'll leave that to you to check out. Also check your answer using a graphing calculator or software such as MATLAB. If you need further help, please ask and I'll detail the answer further.

So.. If I have both local maxima and local minima, there are no vertical tangents or cusps?

I got the derivative part, but I am just not sure about identifying vetical tangents and cusps...
• Jun 6th 2010, 09:31 AM
lilaziz1
Quote:

Originally Posted by dkssudgktpdy
So.. If I have both local maxima and local minima, there are no vertical tangents or cusps?

I got the derivative part, but I am just not sure about identifying vetical tangents and cusps...

To determine any cusps/vertical tangets/corners, take the derivative of the function, and see if there is any point that will make the derivative undefined.
• Jun 6th 2010, 12:54 PM
dkssudgktpdy
Quote:

Originally Posted by lilaziz1
To determine any cusps/vertical tangets/corners, take the derivative of the function, and see if there is any point that will make the derivative undefined.

Ok.. so it means the first question that I wrote does not have both vertical tangent and cusp, right?