posted by Anonymous on .
Consider the function f(x)=6x-cos(x)+5 on the interval 0 is less than or equal to x, and x is less than 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 in non-zero length in each case.
For every k in _______less than or equal to k is less than or equal to _________ there is a c in _________ is less than or equal to c which is less than or equal to________ such as f(c)=k.
Thank you so much! Hopefully someone can figure this out! sorry if the wording is confusing, there are no "less than or equal to" signs on my computer.
Yoiu need f(x) at the endpoints:
f(0) = 4
f(1) = 11-cos(1) = 0.54
For every k in 0.54 <= k <= 4 there is a c in 0 <= c <= 1 such as f(c)=k.
That is, since f(x) changes continuously from 4 to .54, it assume every intermediate value at some point along the interval.