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
Here f (x) = 4x3 – 6x2 – 72x + 30
∴ f ' (x) = 12x2 – 12x – 72 = 12 (x2 – x – 6) = 12 (x – 3) (x + 2)
f '(x) = 0 gives us 12 (x – 3) (x + 2) = 0
∴ x = – 2, 3
The points x = – 2, 3 divide the real line into three disjoint intervals (– ∞ – 2), (–2, 3), (3, ∞).
Interval Sign of f' (x) Nature of function f
(–∞, –2) (–) (–) > 0 f is strictly increasing
(– 2, 3) (–) (+) < 0 f is strictly decreasing
(3, ∞) (+) (+) > 0 f is strictly increasing
(a) f is strictly increasing in the intervals (– ∞, – 2) and (3,
Find the intervals in which the following functions are strictly increasing or strictly decreasing:
– 2x3 – 9x2 – 12x + 1
Long Answer TypeDetermine for which values of x, the function f (x) = x4 – 2x2 is increasing or decreasing.
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