1. Calculus I

Curve Sketching — Quiz

Test your understanding of curve sketching with 5 practice questions.

Practice Questions

Question 1

When sketching a curve, what does a change in the sign of the second derivative, $f''(x)$, indicate?

Question 2

For a function $f(x)$, if $f'(x) = 0$ and $f''(x) > 0$ at a critical point $x=c$, what can be concluded about the point $(c, f(c))$?

Question 3

Consider the function $f(x) = x^3 - 6x^2 + 9x + 1$. To find the critical points, we need to set the first derivative to zero. What are the critical points of this function?

Question 4

Which of the following describes the behavior of a function $f(x)$ if it is 'concave up' over an interval?

Question 5

When determining the horizontal asymptotes of a rational function $f(x) = \frac{P(x)}{Q(x)}$, what is the primary factor to consider?