Question

Verify the Rolle’s theorem for function for the following function f(x)=(x-1)(x-2)(x-3),x(1,3)

​

Answer 1

Step-by-step explanation:

The given function f(x)=x

2

(1−x

2

) on [0,1] is continuous and differentiable on (0,1), since it is a polynomial of degree 4.

Again f(0)=0=f(1).

So f(x) satisfies all the conditions of Rolle's theorem.

According to Rolle's theorem there exists c∈(0,1) such that f

′

(c)=0.

Now f

′

(c)=0 gives

2c−4c

3

=0

or, 2c(1−2c

2

)=0

or, c=

2

1

[ Since c∈(0,1)]

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