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If a , b are two real numbers with a<b ,...

If `a , b` are two real numbers with `a

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The correct Answer is:
4
Let `f(x)=x^(4),xepsilon[a,b]`
`f(x)` satisfies coditions of `LMVT` [as `f(x)` is continuous and differentiable] therefore.
`(f(b)-f(a))/(b-a)=f^(')(c),agtcgtb`
or `(b^(4)-a^(4))/(b-a)=4c^(3)implies((b^(2)+a^(2))(b+a)(b-a))/((b-a)^(c^(3)))=4`
`(b^(3)+a^(3)+ab^(2)+a^(2)b)/(c^(3))=4`
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