Application of Derivatives 4 Question 18

19. Let f,g and h be real-valued functions defined on the interval [0,1] by f(x)=ex2+ex2,g(x)=xex2+ex2 and h(x)=x2ex2+ex2. If a,b and c denote respectively, the absolute maximum of f,g and h on [0,1], then

(2010)

(a) a=b and cb

(b) a=c and ab

(c) ab and cb

(d) a=b=c

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Answer:

Correct Answer: 19. (a)

Solution:

  1. Given function, f(x)=ex2+ex2,g(x)=xex2+ex2 and h(x)=x2ex2+ex2 are strictly increasing on [0,1].

Hence, at x=1, the given function attains absolute maximum all equal to e+1/e.

a=b=c



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