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Rolle's theorem is applicable for the f...

Rolle's theorem is applicable for the function `f(x) = |x-1|` in `[0,2]`.

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For the curve `sqrt(x) + sqrt(y) = 1, (dy)/(dt)` at `(dy)/(dx)` at `((1)/(4),(1)/(4))` is - 1
We have, `sqrt(x) + sqrt(y) = 1`
`rArr (1)/(2sqrt(x)) + (1)/(2sqrt(y)) (dy)/(dx) = 0`
`rArr (dy)/(dx) = - (sqrt(y))/(sqrt(x))`
`:. (dy/dx)_(((1/4,1/4))) = (-1/2)/(1/2) = - 1`
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