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

Question

... do I apply IVT or MVT?

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Answer 1 · 2016-11-14T09:57:23

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

Yes

#abs(cosx)<=1#

The function is strictly decreasing

#f'(x)=cosx-6<=-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.