Consider the function fx1xcosx3 on the interval 0

Consider the function f(x)=1x?cos(x)+3 on the interval 0<(or equal to)x<(or equal to)1. The Intermediate Value Theorem guarantees that there is a value c such that f(c)=k for which values of c and k? Fill in the following mathematical statements, giving an interval with non-zero length in each case.
For every k in _____<k<______,
there is a c in _____<c<______
such that f(c)=k.

Solution

when k=0, f(0)=2, when k=1, f(1)=4-cos(1) For every k in _____2
Consider the function f(x)=1x?cos(x)+3 on the interval 0<(or equal to)x<(or equal to)1. The Intermediate Value Theorem guarantees that there is a value c

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