3.1 Practice

Question 0

Locate the absolute extrema of:

f(x) = 3 - x on [-1, 2]

Answer 0

Maximum: (-1, 4)
Minimum: (2, 1)

Question 1

Find the critical numbers of:

f(x) = 4x / (x^2 + 1)

Answer 1

x = ±1

Question 2

Locate the absolute extrema of:

f(x) = x^2 - 2x on [0, 4]

Answer 2

Minimum: (1, -1)

Maximum (4, 8)

Question 3

Locate the absolute extrema of:

f(x) = x^2 / (x^2 + 3) on [-1,1]

Answer 3

Minimum: (0, 0)
Maximum: (-1, 1/4)
(1, 1/4)

Question 4

Locate the absolute extrema of:

f(x) = 3x^(2/3) - 2x on [-1, 1]

Answer 4

Minimum: (0, 0)
Maximum: (-1, 5)

Question 5

Find the critical numbers of

f(x) = (sinx)^2 +cosx

(0, 2π)

Answer 5

π/3, π, 5π/3