Question

Verify Rolle's theorem for the function
f(x) = x²-4x+10 on [0,4]​

Answer 1

(x)=x

2

−4x+10 ∀ x∈[0,4]

Now, Rolle's theorem states that there exists a c∈[0,4] such that f

′

(c)=0 if f(4)=f(0)

Now, f(4)=10 and f(0)=10. Hence, first condition is satisfied.

Also, on solving the equation,

2c−4=0

∴2c=4

∴c=2

Now, as c∈[0,4], Rolle's theorem is satisfied

Answer 2

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