3.3 Practice

Question 1

Identify the open intervals where the function f(x) = –3x^2 + 5x – 3 is increasing or decreasing.

Answer 1

Increasing: (-∞, 5/6)
Dec: (5/6, ∞)

Question 2

Identify the open intervals on which the function y= 18x − 36cosx, where 0< 2π is increasing or decreasing.

Answer 2

Inc: (0, 7π/6) and (11π/6, 2π)
Dec: (7π/6, 11π/6)

Question 3

Find all relative extrema for f(x) = 4x^3 - 24x^2 + 2.

Answer 3

Relative Max: (0,2)

Relative Min: (4, -126)

Question 4

Find the relative maxima of f(x) = [ cos(5x) ]^2 on the interval (0, 2.513)

Answer 4

Relative Max: (0.628,1),

1. 257,1),
(1. 885,1

Question 5

Find all relative extrema for f(x) = (x - 1)^(4/9)

Answer 5

Relative Min: (1,0)