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If the function f:[0,4] rightarrow R is differentiable then show that: (i) For a,b epsilon(0,4), (f(4))^(2) - (f(0))^(2) = 8f(a) f(b) (ii)int_0^4 f(t)dt =2 [alphaf(alpha^^(2) + betaf(beta^(2))]for some alpha, beta, such that 0

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Answer :(i) `f(a)f(B) for a,b,in (0,4)`
(II) `int_0^4 f(t)dt =2 [alphaf(ALPHA^^(2) + betaf(BETA^(2))]`for some alpha, beta such that `0 ltalpha, beta lt 2`.


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