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Homework Statement
State the Mean Value Theorem and find a point which satisfies the conclusions of the Mean Value Theorem for f(x)=(x-1)3 on the interval [1,4].
2. The attempt at a solution
Mean Value Theorem:states that there exists a c∈(a,b) such that f'(c)=[itex]\frac{f(b)-f(a)}{b-a}[/itex]
3(x-1)2=[itex]\frac{27-0}{4-1}[/itex]
3(x-1)2=[itex]\frac{27}{3}[/itex]
3(x-1)2=9
→(x-1)2=3
→x=1±√3
∴x=1+√3 which lies on the interval [1,4].
I was wondering if I did the question correctly and if there was anything further I should add.
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