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Chapter 4: Q. 3 TB (page 361)

State the Mean Value Theorem.

Short Answer

Expert verified

The mean value theorem state that if a function f is continuous on the interval [a,b]and differentiable on (a,b)then there will be at least one value c that belongs to the interval such that,

f'(c)=f(b)-f(a)b-aWherec∈(a,b)

Step by step solution

01

Step 1. Given information. 

The given theorem whose description is asked is Mean Value Theorem.

02

Step 2. Description.

Mean Value Theorem.

Consider a function f(x)is continuous on the interval role="math" localid="1648623601162" a,band differentiable on a,bthen there will be at least one value c which belongs to the interval such that,

f'(c)=f(b)-f(a)b-aWherec∈(a,b)

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