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Let f:[2,7]to[0,oo) be a continuous and ...

Let `f:[2,7]to[0,oo)` be a continuous and differentiable function. Then show that
`(f(7)-f(2))((f(7))^2+(f(2))^2+f(2)f(7))/3=5f^2(c)f^(prime)(c),` where `c in [2,7]dot`

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