Determine whether or not the graph of f has a vertical tangent or a vertical cusp at c. I don't fully understand how to do it.

(x+3)^4/3; c=-3

I know that you differentiate it

f'(x)=4/3(x+3)^1/3
but I don't know what to do from here.

Question

Determine whether or not the graph of f has a vertical tangent or a vertical cusp at c. I don't fully understand how to do it.

(x+3)^4/3; c=-3

I know that you differentiate it

f'(x)=4/3(x+3)^1/3
but I don't know what to do from here.

anonymous · Answer

Alright, so recall that the derivative is simply the rate of change of a function. When the function it is not changing, it is at a concave point wherein $f'(x) = 0$. When the function is undefined, it has a vertical slope.
When is the function $\frac 4 3 (x+3)^{1/3}$ undefined?

anonymous · Answer

-3

anonymous · Answer

Are you sure?

anonymous · Answer

Honestly, I don't know what to do. Are you saying make the derivative equal to 0?