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Application Of Derivatives

Question
CBSEENMA12035323
Wired Faculty App

Find the intervals in which the following functions are strictly increasing or strictly decreasing:
– 2x3 – 9x2 – 12x + 1

Solution

Let f (x) = – 2x3 – 9x2 – 12x + 1
∴    f ' (x) = – 6x2 – 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 = – 2, – 1 divide the real line into three intervals (– ∞, – 2), (– 2, – 1),
(1) In the interval (– ∞, – 2), f '(x) < 0
∴   f (x) is strictly decreasing in (– ∞, – 2).
(2) In the interval (– 2, – 1), f ' (x) > 0
∴  f (x) is strictly increasing in (– 2, – 1).
(3) In the interval (– 1, ∞), f '(x) < 0
∴  f (x) is strictly decreasing in (– 1, ∞).

Some More Questions From Application of Derivatives Chapter

The radius of a circle is increasing uniformly at the rate of 4 cm per second Find the rate at which the area of the circle is increasing when the radius is 8 cm.

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