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MeIsBella
26.09.2019 •
Mathematics
Last question for tonight. i need solving this problem.
consider the function f(x)=5x−cos(x)+2 on the interval 0≤x≤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.
i've included a picture for reference.
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Ответ:
(j. stewart, “calculus”, 7th ed., brook/coles.)
if you have a function that's is continuous on a closed interval , and a number is an intermediate value between and , then there's some number in the interval that satisfies .
the c is for the x-value or the input value into the function.
the k is for the y-value or the output value of the function at c.
so in this question, we have a continuous function on . the interval in question for the ivt must be then.
k is between the values of the function at the endpoints. so
so for , we need to get the values of the function at the endpoints of the interval to determine the range that k can be in.
and c must be a number in the interval . (your current answers of goes out of the interval originally stated for the function. the c is the x-value or the input value into the function.)
so for every in , there is a in etc.. though i don't know about how many decimal places to round to for
Ответ:
The answer is c)5