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Question

# Verify Rolle's theorem for the function f(x)=10xâˆ’x2 in the interval [0,10]

A
Yes Rolle's theorem is applicable and the stationary point is x=5
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B
Yes Rolle's theorem is applicable and the stationary point is x=4
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C
No Rolle's theorem is not applicable in the given interval
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D
none of these
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Solution

## The correct option is A Yes Rolle's theorem is applicable and the stationary point is x=5f(x)=10x−x2[0,10]10x−x2 is continuous in [0,10] since it is polynomial function.f′(x)=10−2x is defined for all values of x in (0,10)⇒f(x) is differentiable on (0,10)f(0)=f(10)=0∴ There exists a c,a≤c≤b0≤c≤10Such that f′(c)=010−2x=0x=5 5 lies in [0,10]

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