Application of Derivatives 2 Question 10

10. If f(x)=xex(1x), then f(x) is

(2001, 2M)

(a) increasing in [1/2,1]

(b) decreasing in R

(c) increasing in R

(d) decreasing in [1/2,1]

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Solution:

  1. Given, f(x)=xex(1x)

f(x)=ex(1x)+xex(1x)(12x)=ex(1x)[1+x(12x)]=ex(1x)(1+x2x2)=ex(1x)(2x2x1)=ex(1x)(x1)(2x+1)

which is positive in 12,1.

Therefore, f(x) is increasing in 12,1.



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