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Question

If a<0, the function (eax+e-ax)is a decreasing function for all values of x, where


A

x<0

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B

x>0

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C

x<1

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D

x>1

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Solution

The correct option is A

x<0


Finding decreasing function:

Let, f(x)=(eax+e-ax)

Now,

f(x)=(eax+e-ax),a>0Differentiatewithrepecttoxf'(x)=(aeax-ae-ax),a<0Valueoff'(x)<0thereforef'(x)=(aeax-ae-ax)<0(aeax-ae-ax)<0(eax-e-ax)<0(eax<e-ax)forx<0

Hence, correct option is (A)


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