If f(x)=cos|x|−2ax+b𝑓(𝑥)=cos|𝑥|-2𝑎𝑥+𝑏 and function f𝑓 increases for all x𝑥 then find the maximum value of 2a+1
Question
Solution 1
The function f(x) = cos|x| - 2ax + b is increasing for all x. This means the derivative of the function is always positive.
Let's find the derivative of the function:
f'(x) = -sin|x|*sign(x) - 2a
For the function to be increasing, f'(x) > 0 for all x.
-sin|x|*sign(x) - 2a > 0
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