Homework Help: Calculus

Posted by Abigail on Sunday, February 6, 2011 at 3:36pm.

Sorry...
Consider the function f(x) = 8.5 x − cos(x) + 2 on the interval 0 Ём x Ём 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 ____ Ём k Ём___ ,
there is a c in 0 Ём c Ём 1
such that f(c) = k.

Calculus - Abigail, Sunday, February 6, 2011 at 4:25pm
Sorry...
Again...
Before I posted the question, I could see the symbols...
Consider the function f(x) = 8.5 x − cos(x) + 2 on the interval 0 less than or equal to x 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 with non-zero length in each case.

For every k in ______ less than or equal to k less than or equal to ______ ,
there is a c in 0 less than or equal to c less than or equal to 1
such that f(c) = k.
Calculus - MathMate, Sunday, February 6, 2011 at 4:54pm
"Consider the function f(x) = 8.5 x − cos(x) + 2 on the interval 0 less than or equal to x less than or equal to 1.

The Intermediate Value Theorem guarantees that there is a value c such that f(c) = k for 0≤c≤1 and f(0)≤k≤f(1), if f(1)≥f(0), and f(0)≥k≥f(1) if f(1)<f(0)."

In this case, f(0)<f(1), so the first case applies.

P.S.
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≤ & l e ;
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