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Application of Derivatives
Question
Wired Faculty App

Find the intervals in which the following function is decreasing:
f (x) = x3 – 12x

Answer

Here f(x) = x3 – 12x
∴ f ' (x) = 3x2 – 12 = 3 (x2 – 4) = 3 (x – 2) (x + 2)
For f (x) to be decreasing, f ' (x) < 0
∴ 3 (x – 2) (x + 2) < 0 or (x – 2) (x – 2) < 0
∴  – 2 < x < 2
f (x) is decreasing when – 2 < x < 2.

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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.