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Let fa n dg be differentiable on [0,1] s...

Let `fa n dg` be differentiable on [0,1] such that `f(0)=2,g(0),f(1)=6a n dg(1)=2.` Show that there exists `c in (0,1)` such that `f^(prime)(c)=2g^(prime)(c)dot`

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Since, f(x) and g(x) are differentiable functions for `0lexle1`
`:. 'f(c)=(f(1)-f(0))/(1-0)`
Using Lagrange's Mean Value theorem,
`(6.2)/(1-0)4`
and `g'(c)=(g(1)-g(0))/(1-0)`
`=(2-1)/(1-0)=2`
`rArr f'(c)=2g'(c)`
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