Thread: Identifying any cusp or vertical tangents

1. 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)

2. 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 = $2t*e^{3t} + t^2 3e^{3t}$; 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.

3. 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 = $2t*e^{3t} + t^2 3e^{3t}$; 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...

4. 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.

5. 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?

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