Question

verify langrange mean value therom = 2xsquare + 3x-7

Answer 1

$\Large\mathtt\green{ }\huge\underline\mathtt\red{Answer : }$

f(x)=2x2−3x+1 in the interval [1,3]

We know that a polynomial function is continuous everywhere and also differentiable.

So f(x) being a polynomial is continuous and differentiable on (1,3)

So there must exist at least one real number c∈(1,3) such that

f′(c)=3−1f(3)−f(1)=2f(3)−f(1)

We have f(x)=2x2−3x+1

f(1)=2−3+1=0

f(3)=2×9−3×3+1=18−9+1=10

f′(x)=4x−3

f′(c)=4c−3

∴4c−3=210−0

⇒4c−3=5

⇒4c=8

⇒c=2

∴c∈(1,3)

Hence Lagrange's Mean Value theorem is verified.

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Answer 2

Answer:

verify langrange mean value therom = 2xsquare + 3x-7

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