$\displaystyle y = x cosx$
How do I find when is the slope of the tangent equal to zero?
Equivalently, the derivative is equal to 0.
So, we calculate the derivative:
$\displaystyle \frac{d}{dx} x \cos x = -x \sin x + \cos x$
Then we set it equal to 0:
$\displaystyle \cos x - x \sin x = 0$
$\displaystyle \cos x = x \sin x$
$\displaystyle \frac{\cos x}{\sin x} = x$
$\displaystyle \cot x = x$