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Application Of Derivatives

Question
CBSEENMA12035347
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Find the intervals in which the following function is increasing or decreasing
f (x) = (x + 2) e–x 

Solution

f (x) = (x + 2) e–x
∴  f ' (x) = (x + 2) · e–x (– 1) + e–x · 1 = e–x (– x – 2 + 1)
∴  f ' (x) = – (x + 1) e–x
For f (x) to be increasing
f ' (x) > 0 ⇒ –(x + 1) e–x > 0
⇒ (x + 1) e–x < 0 ⇒ x + 1< 0 [∵ e–x > 0]
⇒ x < – 1
∴  f (x) is increasing in ( – ∞ , – 1)
For f (x) to be decreasing,
f ' (x)  < 0  ⇒   – (x + 1) e–x < 0
⇒ (x + 1) e–x > 0 ⇒ x + 1 > 0 [ ∵ c–x > 0]
⇒ x > – 1
∴  f (x) is 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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