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Question

Verify Rolle's theorem for the function f(x)=10xx2 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=5
f(x)=10xx2[0,10]
10xx2 is continuous in [0,10] since it is polynomial function.
f(x)=102x 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,acb
0c10
Such that
f(c)=0
102x=0
x=5 5 lies in [0,10]

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