Finding maximum and minimum values of $\mathrm{sin}\left(2x\right)-x\text{}\text{for}\text{}x\in [-\frac{\pi}{2},\frac{\pi}{2}]$

Octavio Miller
2022-01-27
Answered

Finding maximum and minimum values of $\mathrm{sin}\left(2x\right)-x\text{}\text{for}\text{}x\in [-\frac{\pi}{2},\frac{\pi}{2}]$

You can still ask an expert for help

search633504

Answered 2022-01-28
Author has **16** answers

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.

You get

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.

asked 2021-08-20

Let P(x, y) be the terminal point on the unit circle determined by t. Then

asked 2022-04-09

How to show

$\mathrm{ln}(\mathrm{tan}\left(x\right)+\mathrm{sec}\left(x\right))=\frac{\mathrm{ln}(1+\mathrm{sin}x)-\mathrm{ln}(1-\mathrm{sin}x)}{2}$ is true or false

asked 2022-01-03

Im

asked 2022-03-01

How can I calculate

$\mathrm{sin}({10}^{{10}^{100}}-10)$ ?

asked 2022-02-27

How to prove it?

$2\mathrm{sin}x\le x-\frac{\pi}{3}+\sqrt{3}$

asked 2022-01-17

Finding n if $\left|\sum _{r=0}^{3n-1}{\beta}^{{2}^{r}}\right|=4\sqrt{2}$ where $\beta =\mathrm{exp}\left(\frac{i2\pi}{7}\right)$

asked 2022-05-02

Proving Trig/Calc Identity $\frac{1}{1-\mathrm{sin}\left(x\right)}=\frac{1+\mathrm{sin}x}{{\mathrm{cos}\left(x\right)}^{2}}$