1
Maximum and Minimum Values- HW Problems
Find the critical point for:
1. 𝑓(𝑥 ) = 𝑥 3 − 4𝑥 2
2. 𝑔(𝑥 ) = 𝑥 4 − 4𝑥 2
2
3. 𝑓(𝑥 ) = 2 − 𝑥 3
Find the absolute maximum and minimum values on each interval.
4. 𝑓(𝑥 ) = 𝑥 3 − 3𝑥 2 [−2, 3]
5. 𝑓(𝑥 ) = 𝑥 3 − 6𝑥 2 + 5 [−1, 5]
2
6. 𝑓(𝑥 ) = 3 + 𝑥 3 [−1, 1]
𝑥2
7. 𝑔(𝑥 ) = [−2, 2]
𝑥2 +4
16
8. 𝑓(𝑥 ) = 𝑥 2 + [1, 4]
𝑥
5 2
9. 𝑓(𝑥 ) = 3𝑥 + 60𝑥
3 3 [−1, 1]
𝜋
10. 𝑔(𝑥 ) = sin(2𝑥 ) + 2 cos(𝑥 ) [0, ]
2
Maximum and Minimum Values- HW Problems
Find the critical point for:
1. 𝑓(𝑥 ) = 𝑥 3 − 4𝑥 2
2. 𝑔(𝑥 ) = 𝑥 4 − 4𝑥 2
2
3. 𝑓(𝑥 ) = 2 − 𝑥 3
Find the absolute maximum and minimum values on each interval.
4. 𝑓(𝑥 ) = 𝑥 3 − 3𝑥 2 [−2, 3]
5. 𝑓(𝑥 ) = 𝑥 3 − 6𝑥 2 + 5 [−1, 5]
2
6. 𝑓(𝑥 ) = 3 + 𝑥 3 [−1, 1]
𝑥2
7. 𝑔(𝑥 ) = [−2, 2]
𝑥2 +4
16
8. 𝑓(𝑥 ) = 𝑥 2 + [1, 4]
𝑥
5 2
9. 𝑓(𝑥 ) = 3𝑥 + 60𝑥
3 3 [−1, 1]
𝜋
10. 𝑔(𝑥 ) = sin(2𝑥 ) + 2 cos(𝑥 ) [0, ]
2
