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Let f(x) = Max. {x^2, (1 - x)^2, 2x(1 -...

Let f(x) = Max. `{x^2, (1 - x)^2, 2x(1 - x)} where x in [0, 1]` If Rolle's theorem is applicable for f(x) on largestpossible interval [a, b] then the value of `2(a+b+c)` when `c in [a, b]` such that f'(c) = 0, is

A

`(2)/(3)`

B

`(1)/(3)`

C

`(1)/(2),`

D

`(3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
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ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Passage Based Questions)
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  3. Let f(x) = Max. {x^2, (1 - x)^2, 2x(1 - x)} where x in [0, 1] If Rol...

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  4. Consider the function f(x)=max x^(2), [((1-x)^(2),2x(1-x))],x in [0,1]...

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  13. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3)andf(x)=sqrt(g(x)),f(x) have it...

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