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Chapter 4: Q. 3 (page 384)

State the Intermediate Value Theorem, and illustrate the theorem with a graph.

Short Answer

Expert verified

Themeaningbehindtheintermediatevaluetheoremis,whengraphischangefrompositivetonegative,itmustcrossx-axis.

Step by step solution

01

Step 1. Given information is:

If f is continuous on [a,b] and f(a) and f(b) are having opposite signs, then there exist at least one point c in [a,b] such that f(c)=0

02

Step 2. Graph and Theorem

Considertheabovegraph,f(a)ispositiveandf(b)isnegative,thereexistapointcsuchthatf(c)=0.Themeaningbehindtheintermediatevaluetheoremis,whengraphischangefrompositivetonegative,itmustcrossx-axis.

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