maths

MATH 101 COLLEGE MATHEMATICS

FINAL EXAM

1. Find 𝑓 ′(2) if

𝑓(𝑥) = 𝑥2

√1 + 𝑥3

2. Find the absolute maximum and minimum of

𝑓(𝑥) = 𝑥3 − 12𝑥

over the interval [-3, 3].

3. Find the following antiderivative

∫ 𝑥 + 2

√𝑥 + 1 𝑑𝑥

4. Find the value of k if

∫ 1

√𝑥𝑘 3

1

0

𝑑𝑥 = 3

5. Find the following antiderivative

∫ 𝑥2√1 + 𝑥3 𝑑𝑥 1

0

6. Find the area of the region between

𝑦 = 𝑥3 + 3𝑥

and

𝑦 = 4𝑥

(note: The region consists of two parts. Consider them separately.)