3. Differentiation

Curve Sketching — Quiz

Test your understanding of curve sketching with 5 practice questions.

Practice Questions

Question 1

For the function $f(x) = x^3 - 3x^2 + 4$, what is the first derivative $f'(x)$?

Question 2

Given $f'(x) = 2x - 4$, what are the critical points of $f(x)$?

Question 3

If $f''(x) = 6x - 6$, what is the inflection point of $f(x)$?

Question 4

For the function $f(x) = x^4 - 4x^3 + 6x^2$, what is the second derivative $f''(x)$?

Question 5

At which point does the function $f(x) = x^3 - 3x + 2$ have a local maximum?