Application of Derivatives 4 Question 39

41. Let g(x)=0exf(t)1+t2dt. Which of the following is true?

(a) g(x) is positive on (,0) and negative on (0,)

(b) g(x) is negative on (,0) and positive on (0,)

(c) g(x) changes sign on both (,0) and (0,)

(d) g(x) does not change sign (,)

Analytical & Descriptive Questions

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Answer:

Correct Answer: 41. a=14,b=54;f(x)=14x254x+2

Solution:

  1. g(x)=f(ex)1+(ex)2ex

=2ae2x1(e2x+aex+1)2ex1+e2x

g(x)=0, if e2x1=0, i.e. x=0

If

x<0,e2x<1g(x)<0



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