5. Analytical Applications of Differentiation

Connecting A Function, Its First Derivative, And Its Second Derivative — Quiz

Test your understanding of connecting a function, its first derivative, and its second derivative with 5 practice questions.

Practice Questions

Question 1

If a function $f$ is increasing on an interval, what can be said about its first derivative on that interval when it exists?

Question 2

What does it mean if $f''(x) > 0$ on an interval?

Question 3

A function $f$ has $f'(a) = 0$ and $f''(a) < 0$. What is the most likely conclusion about $f$ at $x = a$?

Question 4

What condition must hold for a point to be an inflection point of $f$?

Question 5

If $f'(x) < 0$ and $f''(x) > 0$ on an interval, which description fits $f$ on that interval?