Use the Intermediate Value Theorem and the Mean Value Theorem to prove that the equation cos...

Use the Intermediate Value Theorem and the Mean Value Theorem to prove that the equation cos (x) = -10x has exactly one real root.

Not permitted to use words like "Nope", "Why?", or "aerkewmwrt".

Will be glad if you can help me with this question, will like to add some of your points to the one I have already summed up.. Thanks

Expert Solution

1) According to intermediate value theorem if a continuous function, f, with an interval, [a, b], as its domain, takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval..

In other word if then

We can conclude from above theorem : If a continuous function has values of opposite sign inside an interval, then it has at least root in that interval

Mean value theorem (MVT)

Suppose f(x) is a real valued function in the interval [a,b] which satisfies both of the following condition.

f(x) is continuous on the closed interval [a,b].
f(x) is differentiable on the open interval (a,b).

Then there is a number c in the interval (a,b) i.e. a < c < b such that

milcah answered 2 years ago

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