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the number of real values of x where the function f(x) = cosx+cos{(√2)x} attains its maximum is (a) 0 (b) 1 (c) 2 (d) infinite

 the number of real values of x where the function f(x) = cosx+cos{(√2)x} attains its maximum is


(a) 0


(b) 1


(c) 2


(d) infinite

Grade:12

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear raman malik.

f(x) = cosx+cos{(√2)x}

f'(x)=-sin x -√2 sin √2x =0

    it gives x= 2m ∏/(√2 +1 )   and  (2m +1 ) ∏  /(√2 -1)  where m is any natural number

  clearly both values are not multiple of 2∏

only for m=0 

and f(0) = 1+1 =2 is its maximum value

so only one solution option b is correct

Please feel free to post as many doubts on our discussion forum as you can.
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Regards,
Askiitians Experts
Badiuddin

 

  

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