# How do you find critical points for the equation (7/10)cos(x/10)?

Jun 25, 2018

$x = 10 k \pi$ where $k$ is an integer.

#### Explanation:

$f \left(x\right) = \frac{7}{10} \cos \left(\frac{x}{10}\right)$

Critical points are when derivative is 0 or undefined.

$f ' \left(x\right) = - \frac{7}{100} \sin \left(\frac{x}{10}\right)$

Sin is well defined at every point but is equal to zero at 0,$\pi$

$- \frac{7}{100} \sin \left(\frac{x}{10}\right) = 0$

#sin(x/10)=0

$\sin \left(y\right) = 0$ at $y = k \pi$

Therefore

$\sin \left(\frac{x}{10}\right) = 0$ at $\frac{x}{10} = k \pi$ so $x = 10 k \pi$ where $k$ in an integer.