5. Analytical Applications of Differentiation

Determining Concavity Of Functions Over Their Domains — Quiz

Test your understanding of determining concavity of functions over their domains with 5 practice questions.

Practice Questions

Question 1

What does it mean for a function to be concave up on an interval?

Question 2

If $f''(x) < 0$ for all $x$ in an interval, what can be concluded about the graph of $f$ on that interval?

Question 3

A function changes concavity at a point where $f''(x)$ changes sign. What is this point called?

Question 4

Suppose $f'(x) = 0$ at $x = c$ and $f''(c) > 0$. What does the second derivative test tell you?

Question 5

For the function $f(x) = x^3$, on which interval is the graph concave down?