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
Let f (x) = 2x3 – 9x2 + 12x + 30
∴ f '(x) = 6 x2 – 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 = 1, 2 divide the real line into three intervals (– ∞, 1), (1, 2), (2, ∞)
1. In the interval (– ∞, 1), f ' (x) > 0
∴ f (x) is increasing in ( – ∞, 1)
2. In the interval (1, 2), f ' (x) < 0
∴ f(x) is decreasing in (1, 2)
3. In the interval (2, ∞). f ' (x) > 0
∴ f (x) is increasing in (2, ∞)
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
Long Answer TypeDetermine for which values of x, the function f (x) = x4 – 2x2 is increasing or decreasing.
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