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Verify Lagranges mean value theorem f...

Verify Lagranges mean value theorem for function `f(x)=2x-x^2` on `[0,\ 1]` and find a point `' c '` in the indicated interval:

Text Solution

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Lagrange's theorem is only applicable if function is continuous in `[0, 1]`, differentiable in `(0, 1)`

and There exist `c in (0, 1)` such that `f'(c)=(f(b)-f(a))/(b-a)`

`f'(x)=2-2x`

`f'(c)=2-2c=(f(1)-f(0))/(1-0)`

`2-2c=(2-1-0)/(1-0)`

`2-2c=1`

`c=1/2 in (0,1)`

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