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.
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
Let f (x) = 6 + 12x + 3x2 – 2x3 = – 2x3 + 3x2 + 12x + 6
∴ f ' (x) = – 6x2 + 6x + 12 = – 6 (x2 – x – 2) = – 6 (x + 1 ) (x – 2)
(a) For f (x) to be increasing, f ' (x) > 0
or – 6 (x + 1) (x – 2) > 0 or (x + 1) (x – 2) < 0
⇒ – 1 < x < 2
∴ f (x) is increasing for –1 < x < 2
(b) For f (x) to be decreasing , f ' (x) < 0
or – 6 (x + 1) (x – 2) < 0 or (x + 1) (– 2) > 0
⇒ either x < – 1 or x > 2
∴ f (x) is decreasing for x < – 1 or x > 2.
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