Application of Derivatives 2 Question 12

####12. Let f(x)=∫ex(x−1)(x−2)dx. Then, f decreases in the interval

(a) (−∞,−2)

(b) (−2,−1)

(c) (1,2)

(d) (2,∞)

(2000, 2M)

Show Answer

Answer:

(b)

Solution:

  1. Let

f(x)=∫ex(x−1)(x−2)dxf′(x)=ex(x−1)(x−2)+−++2

⇒f′(x)=ex(x−1)(x−2)

∴f′(x)<0 for 1<x<2

⇒f(x) is decreasing for x∈(1,2).

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