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mr.tea
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Homework Statement
Determine, for each real value of k, the number of solutions in [0,2pi] of:
x+sqrt(2)cos(x)=k
And there is a hint: pi<4(1+sqrt(2))/3
Homework Equations
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The Attempt at a Solution
I tried to define a function f(x)=x+sqrt(2)cos(x)-k and to find the number of zeros for the derivative that will give me(using Rolle's Theorem) the maximum number of zeros to the function. That really didn't help since I got that there are 2 zeros to the derivative, which mean at most 4 zeros to the function.
I also thought to use intermediate value theorem but it's no useful since k is unknown.
Thank you,
Thomas
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