For each of the following problems the intervals of increase/decrease are given for a "nice"function f(x) on a specified domain. Determine the relative/local extrema and global/absolute extrema (if possible)
- f is defined on [0, 10], f is increasing on [0, 4], decreasing on [4, 7], and increasing on [7, 10].
- f is defined for all real numbers (-∞, ∞), f is decreasing on (-∞, -1], increasing on [-1, 0], increasing on [0, 3], and decreasing on [3, ∞).
- f is defined for all real numbers, f is increasing on (-∞, -1], decreasing on [-1, 1], increasing on [1, 4.6], decreasing on [4.6, 10.113], and increasing on [10.113, ∞).
- f is defined on [0, π2 π + √ 7], f is decreasing on [0, π], increasing on [π, π2 - √ 2], and decreasing on [π2 - √ 2, π2 π + √ 7].
- f is defined on [-1, 20], f is decreasing on [-1, 3.35] and increasing on [3.35, 20], f(-1) = 10, f( 20 ) = 9.7326.
- f is defined on [0, 20], f is increasing on [0, 2], decreasing on [2, 5], decreasing on [5, 7], increasing on [7, 17], and decreasing on [17, 20], f(0) = 10, f(2) = 12, f(7) = 1, f(17) = 8, f(20) = 5.
- f is defined on [0, 20], f is decreasing on [0, 4], increasing on [4, 10], decreasing on [10, 13], and increasing on [13, 20], f(0) = 20.134, f(10) = 24.7364, f(13) > f(0), f(20) > f(10).
- f is defined on [0, 10], f is decreasing on [0, 9.345] and decreasing on [9.345, 10].
- f is defined on [0, 10], f is holding constant on [0, 3], increasing on [3, 8.2], and decreasing on [8.2, 10], f( 1.245) > f(9.875).
- f is defined on [0, 2π], f is increasing on [0, π/2], decreasing on [π/2, π], decreasing on [π, 3π/2], and increasing on [3π/2, 2π], f(0) = f(2π).