# Thread: Concavities

1. ## Concavities

When concavities are equal to a number or a constant, what does it mean?

For example, f''(x) = 3, and f''(x) = 0 when x = 2. What does 2 = 3 mean? And when it is f''(2) = 0 it is a point of inflection correct?

2. Originally Posted by Barthayn
When concavities are equal to a number or a constant, what does it mean?

For example, f''(x) = 3, and f''(x) = 0 when x = 2. What does 2 = 3 mean? And when it is f''(2) = 0 it is a point of inflection correct?
f''(2) cannot equal 3 and 0 for the same value of x. That's a contradiction. As a result, both of your sentences "For example, f''(x) = 3, and f''(x) = 0 when x = 2." and "What does 2 = 3 mean?" are meaningless.

The second derivative being zero does not imply that there is a point of inflection. If you know you have a point of inflection, then the second derivative is zero. So the implication only works one way. My favorite mnemonic device for remembering the second derivative test is the following:

I can answer you better if you refine your questions.

3. Originally Posted by Ackbeet
f''(2) cannot equal 3 and 0 for the same value of x. That's a contradiction. As a result, both of your sentences "For example, f''(x) = 3, and f''(x) = 0 when x = 2." and "What does 2 = 3 mean?" are meaningless.

The second derivative being zero does not imply that there is a point of inflection. If you know you have a point of inflection, then the second derivative is zero. So the implication only works one way. My favorite mnemonic device for remembering the second derivative test is the following:

I can answer you better if you refine your questions.
Sorry, when I stated the two examples of f''(x) being equal to something, I meant two different f''(x)'s, not both the same. So If it does not have an x-value, what does it mean?