Math Archive (10)

Calculus Level 4

Consider the function f ( x ) = ∣ x 2 − 7 x + 12 ∣ ( x 2 − 7 x + 10 ) ( x 2 − 4 x + 3 ) f(x)=|x^{2}-7x+12|(x^{2}-7x+10)(x^{2}-4x+3) Then rolle's theorem for f ( x ) f(x) is not applicable to which of the following range?

[ 1 , 3 ] [1,3] [ 3 , 5 ] [3,5] None of these [ 2 , 4 ] [2,4]

Shivam Jadhav by Shivam Jadhav , 22, India

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1 solution

Pranav Rao
May 5, 2016

The given function is {(x-3)|(x-3)|}×(|x-4|)×(x-1)(x-2)(x-5). The function is differentiable at all x except at 4. So rolles theorum is not applicable to the function for the interval [3,5].

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