A parabola opens down, and has a hole at point (-2, 3). Which of the following statements represents the graph?
a) The graph is discontinuous, but differentiable at x = -2
b) The graph is discontinuous, and not differentiable at x = -2
c) The graph is continuous and differentiable at x = -2
d) The graph is continuous, but not differentiable at x = -2
2007-05-11 04:38:22 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Hi,
There are cases where you will not have a derivative. These functions are called non-differentiable. They are as follows:
1. Vertical tangent lines. This is where the slope (m) is undefined.
2. Discontinuities. This is where you have a hole or a vertical asymptote. The function may be differentiable everywhere except at the point it is discontinuous. But, as a whole, the function is non-differentiable.
THIS IS YOUR SITUATION.
3. At cusps. These are sharp corners in a function. These represent a sudden change. For example, you are traveling in your car at a given point in time going 55 mph. In a split second, you are going the opposite direction about 55 mph. An example of this type of graphical behavior is seen in the function f(x) = x^(2/3).
So, the answer is B!
I hope that helps!! :-)
2007-05-11 04:48:29 · answer #1 · answered by Pi R Squared 7 · 1⤊ 0⤋
If it's differentiable, then it's continuous, but it's not continuous because f(-2) does not exist, so it's not differentiable either.
2007-05-11 11:49:09 · answer #2 · answered by Philo 7 · 0⤊ 0⤋
b
2007-05-11 11:41:27 · answer #3 · answered by Anonymous · 1⤊ 0⤋
the answer is A
2007-05-11 11:42:09 · answer #4 · answered by autumn p 1 · 0⤊ 1⤋
D- but this is not a real world problem.
2007-05-11 11:42:04 · answer #5 · answered by Grant d 4 · 1⤊ 2⤋
e) do your own homework/test/quiz.
2007-05-11 11:40:49 · answer #6 · answered by Anonymous · 0⤊ 2⤋
B.
2007-05-11 11:41:06 · answer #7 · answered by EIU DUDE 3 · 1⤊ 0⤋