# Homework Help: Behavior of a graph at a point

1. Jan 2, 2006

### Jacobpm64

Which of the following describes the behavior of y = cubicroot(x + 2) at x = -2

(A) differentiable
(B) corner
(C) cusp
(D) vertical tangent
(E) discontinuity

well i graphed the function, and i'm not sure.. i know for sure it isn't E... because f(-2) = 0... it has a value.. uhmm.. as for the rest i'm not sure.. i don't even know what a corner and a cusp is.

2. Jan 2, 2006

### Mindscrape

Well, a cusp is when the second derivative of the function (which measures curvature) decreases or increases on both sides, making an upside down v or right-side up v.

A corner can be described if f is not differential at any point where the secant lines have different limits as they approach a point (it looks like a corner). So can vertical tangency (if point looks like it's derivative would be vertical).

If I were you I would look at what it cannot be.

Last edited: Jan 2, 2006
3. Jan 2, 2006

### Jacobpm64

as for corner.. that just completely and utterly confuses me ;\

let's see..

so, hmm... we know it isn'tA, we aren't sure about B, we know it can't be C, we know it is D, and we know it can't be E..

So we're left with Discussions about B..

am i correct thus far?

Last edited: Jan 2, 2006
4. Jan 2, 2006

### HallsofIvy

A "corner" occurs when the derivative does not exit- but the limits of the derivatives from above and below exist but are different. A "cusp" occurs when the two one sided limits of the derivative do not exist.

5. Jan 3, 2006

### Jacobpm64

so it's none of those... and the answer is only a vertical tangent