Short Answer TypeFind the intervals in which the following functions are strictly increasing or strictly decreasing:
2x3 – 8x2 + 10x + 5
Find the intervals in which the following functions are strictly increasing or strictly decreasing:
2x3 – 6x2 – 48x + 17
Find the intervals in which the following functions are strictly increasing or strictly decreasing:
f (x) = 2x3 – 9x2 + 12x + 30
Find the intervals in which the following functions are strictly increasing or strictly decreasing:
f (x) = 2x3 – 3x2 – 36x + 7
Find the intervals in which the following functions are strictly increasing or strictly decreasing:
f(x) = 2x3 – 21x2 + 36x – 40
Find the intervals in which the following functions are strictly increasing or strictly decreasing:
4x3 – 6x2 – 72x + 30
Find the intervals in which the following functions are strictly increasing or strictly decreasing:
– 2x3 – 9x2 – 12x + 1
Let f (x) = – 2x3 – 9x2 – 12x + 1
∴ f ' (x) = – 6x2 – 18x – 12 = – 6 (x2 + 3x + 2) = – 6 (x + 1) (x + 2)
f '(x) = 0 gives us – 6 (x + 1) (x + 2) = 0 ⇒ x = – 1, – 2
The points x = – 2, – 1 divide the real line into three intervals (– ∞, – 2), (– 2, – 1),
(1) In the interval (– ∞, – 2), f '(x) < 0
∴ f (x) is strictly decreasing in (– ∞, – 2).
(2) In the interval (– 2, – 1), f ' (x) > 0
∴ f (x) is strictly increasing in (– 2, – 1).
(3) In the interval (– 1, ∞), f '(x) < 0
∴ f (x) is strictly decreasing in (– 1, ∞).
Long Answer TypeDetermine for which values of x, the function f (x) = x4 – 2x2 is increasing or decreasing.
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