The shortest distance between line y-x=1 and curve `x=y^2` is

Explanation

Let `A(t-1,t)` is the point on the given line and `B(t^2,t)` is the point on the given curve.

`:. AB = sqrt((t^2-t+1)^2+(t-t)^2)`

`=>AB = t^2-t+1`

`:. f(t) = t^2-t+1`

For minimum or maximum value, `f'(t)` should be `0`.

`f'(t) = 2t-1 = 0`

`=>t = 1/2`

For minimum value `f''(t)` should be more than `0`.

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