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If f:[-5,5]vecR is differentiable functi...

If `f:[-5,5]vecR` is differentiable function and if`f^(prime)(x)` does not vanish anywhere, then prove that `f(-5)!=f(5)dot`

Text Solution

Verified by Experts

If `f(-5)=f(5)`
then there exists at least one point c in the interval (-5 , 5) such that `f'(c)=0`
but it is given that `f'(x) ne 0 AA in (-5, 5)`
` :. f(-5) ne f(5)`
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