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No of values of x where the function attains its maximum . Eq in image

No of values of x where the function attains its maximum . 
Eq in image 

Question Image
Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

f(x) = cos(x) + cos(\sqrt{2}x)
Function will always attain maxima at x = zero.
f'(x) = -sin(x) -\sqrt{2}sin(\sqrt{2}x)
f'(x) = -sin(x) -\sqrt{2}sin(\sqrt{2}x) = 0
-sin(x) -\sqrt{2}sin(\sqrt{2}x) = 0
sin(x) = -\sqrt{2}sin(\sqrt{2}x)
You can calculate the value of x from here......(1)
f''(x) = -cos(x) -2cos(\sqrt{2}x)
Then put the value of x from (1) in here.
If f’’(x) < 0
Thats all the value of x for maxima.
You need to provide interval in which you want to know the number of values.

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