# Finding maximum and minimum values of \sin(2x) - x \text{

Finding maximum and minimum values of
You can still ask an expert for help

## Want to know more about Trigonometry?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

search633504
First differentiate $y=\mathrm{sin}\left(2x\right)-x$
You get ${y}^{\prime }=2\mathrm{cos}\left(2x\right)-1$.At an extrema this value will be zero. So equate the above equation to zero and solve for x. Remember the value of x has to lie in the given interval. It can be seen easily that the $x=\frac{\pi }{6}$
Then find the second derivative of y.
Substitute this value of x obtained.
If the resulting value is positive then the function has a minima at that x.
If it is negative then the function has a maxima.