MATH110 Practice Problem Set #11
1. For 𝑓(𝑥) = 4𝑥 ! − 15𝑥 " − 3𝑥 + 12
a. Find the critical points
b. Find where the function is increasing/decreasing
c. Use the first derivative to find extrema.
d. Identify where function is concave up/down
e. Use second derivative test to find extrema
f. Note any inflection points (changes from concave up to down or vice versa)
g. Check lim 𝑓(𝑥)
#→±&
h. Find all relative and absolute extrema
i. Sketch the function
!
2. Repeat exercise 1 for 𝑓(𝑥) = 𝑥 − 3𝑥 "
3. Repeat exercise 1 for 𝑓(𝑥) = 3 sin 𝑥 − sin! 𝑥
𝑜𝑛 [0,2𝜋]
4. Repeat exercise 1 for 𝑓(𝑥) = cos 2𝑥 − 4 sin 𝑥
𝑜𝑛 [−𝜋, 𝜋]
##
5. Repeat exercise 1 for 𝑓(𝑥) = # # '"#'(
#
6. Repeat exercise 1 for 𝑓(𝑥) = # # '()
7. Find the absolute extrema for the function in question 6 on [−1,1]
8. Repeat exercise 1 for 𝑓(𝑥) = 𝑥√8 − 𝑥 "