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
Let f (x) = 2x3 – 6x2– 48x + 17
∴ f ' (x) = 6x2 – 12x – 48 = 6 (x2 – 2x – 8) = 6 (x + 2) (x – 4)
For f (x) to be increasing,
f ' (x) > 0 ⇒ 6 (x + 2) (x – 4) > 0
⇒ (x + 2) (x – 4) > 0
∴ either x < – 2 or x > 4
∴ f (x) is increasing in (– ∞, 2) ∪ (4, ∞)
For f (x) to be decreasing,
f ' (x) < 0 ⇒ 6 (x + 2) (x – 4) = 0
⇒ (x + 2) (x – 4) < 0 ⇒ – 2 < x < 4
∴ f (x) is decreasing in (– 2, 4)
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
Long Answer TypeDetermine for which values of x, the function f (x) = x4 – 2x2 is increasing or decreasing.
Switch
, is
