# Show that the equation \sin(x)-6x=0 has exactly one root...?

## ... do I apply IVT or MVT?

Nov 14, 2016

graph{(sinx-y)(6x-y)=0 [-10, 10, -5, 5]}

Yes

#### Explanation:

$\left\mid \cos x \right\mid \le 1$

The function is strictly decreasing

$f ' \left(x\right) = \cos x - 6 \le - 5$

So it can be 0 or 1 root (if it has 2 roots there would be a point between roots where $f ' = 0$).

0 is a root.