Question

How would you write open intervals for concavity? After you find the second derivative of a fuction; How would you go about finding the concavity

Answer 1

concave up when f"(x) > 0

Answer 2

I understand that. But when writing the concavity intercals do you use the critical numbers or the points choosen around the critical numbers to denote the up and down? For instance This question

Determin the open intervals on which the graph of of 3x^2+7x-3 is concve up or concve down and I have the derivative as 6x-7 and the crtical number as -7/6; where do I go from there?

Answer 3

critical numbers have nothing to do with concavity. They are used for determining min/max, or where f(x) is undefined.

For your f(x) above, f"(x) = 6, which is always positive.

Makes sense, since the curve is a parabola which opens upward, and is thus always concave up.

Don't forget your algebra I when using calculus.