Short Answer TypeFind the intervals in which the following functions are strictly increasing or decreasing:
6 – 9x – x 2
Find the intervals in which the following function is increasing or decreasing:
x3 – 6x2 + 9x + 15.
Let f (x) = x3- 6x2 + 9x + 15
∴ f '(x) – 3x2 – 12x + 9 = 3 (x2 – 4 x + 3) = 3 (x – 1) (x – 3)
f ' (x) = 0 gives us 3(x – 1) (x – 3) = 0
∴ x = 1, 3
The points x = 1, 3 divide the real line into three intervals (– ∞, 1), (1, 3), (3, ∞).
(1) In the interval (– ∞ , 1), f ' (x) > 0
∴ f (x) is increasing in (– ∞, 1)
(2) In the interval (1, 3), f ' (x) < 0
∴ f ' (x) is decreasing in (1, 3).
(3) In the interval (3, ∞), f ' (x) > 0
∴ f (x) is increasing in (3, ∞).
Find the intervals in which the following function f(x) is
(a) increasing (b) decreasing:
f (x) = 2x3 – 9x2 + 12x + 15
Determine the values of x for which the function f(x) = 2x3 – 24x + 5 is increasing or decreasing.
Find the intervals in which the functions f (x) = 2x3 – 15x2 + 36x + 1 is strictly increasing or decreasing. Also find the points on which the tangents are parallel to the x-axis.
Find the intervals in which the function
f(x) = x3 – 12x2 + 36x + 17 is
(a) strictly increasing (b) strictly decreasing
Find the intervals in which the function f (x) = 2x3 – 15x2 + 36x + 1 is
(a) strictly increasing (b) strictly decreasing
Find the intervals in which the following functions are strictly increasing or strictly decreasing:
x3 – 6x2 – 36x +4
Find the intervals in which the following functions are strictly increasing or strictly decreasing:
2x3 – 15x2 + 36x + 6
Find the intervals in which the following functions are strictly increasing or strictly decreasing:
6 + 12x + 3x2 – 2x3
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