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What is an intermediate value theorem?

Calculus
Tutor: None Selected Time limit: 1 Day

Some examples and ways to solve them sill be nice.

Thanks.

Oct 5th, 2014

If the function f(x) is continuous and if f(a) < f(b) , then there exists at least one value c such that f(a)<f(c)<f(b) where a < c < b

Consider the function x^3-2x-3

f(1) =1^3-2*1-3 =1-2-3=-4

f(2) =2^3-2*2-3 =8-4-3=1

There exists a c between 1 and 2 such that f(c)=0

In fact that value is 1.8934

x y
1 -4
2 1
1.5 -2.625
1.9 0.059
1.8 -0.768
1.85 -0.36837
1.88 -0.11533
1.89 -0.02873
1.895 0.014992
1.896 0.023771
1.894 0.006225
1.893 -0.00253
1.8935 0.001846
1.8934 0.00097

Oct 5th, 2014

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