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
Here f (x) = 2x3 – 3x2 – 36x + 7
∴  f ' (x) = 6x2 – 6x – 36 = 6 (x2 – x – 6) = 6 (x + 2) (x – 3)
f ' (x) = 0 gives us 6 (x + 2) (x – 3)
∴  x = – 2, 3
The points x = – 2, 3 divide the real line into three intervals (– ∞, – 2), (– 2, 3), (3, ∞).
In the interval (– ∞, – 2), f ' (x) > 0
strictly  ∴ f (x) is strictly increasing in (– ∞, – 2)
In the interval (– 2, 3), f ' (x) < 0 ∞ f (x) is strictly decreasing in ( – 2, 3)
In the interval (3, ∞), f ' (x) > 0
∴  f (x) is strictly increasing in (3, ∞)
∴  we see that f (x) is strictly increasing in (– 8, – 2) ∪ (3, ∞) and strictly decreasing in ( – 2, 3)
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Find the intervals in which the following functions are strictly increasing or strictly decreasing:
f(x) = 2x3 – 21x2 + 36x – 40Â
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
Long Answer TypeFind the intervals in which the function f is given by 
(i) increasing   (ii) decreasing
Determine for which values of x, the function f (x) = x4 – 2x2 is increasing or decreasing.
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