At what point of the curve `y=x^2` does the tangent make an angle of `45o` with the x-axis?

Answer

Point is `(1 / 4,1 / 2)`

Explanation

Given, Slope of the tangent `=m=\tan 45^{\circ}=1`


`y^{2}=x`


`2 y( dy / dx)=1`


`dy / dx=1 / (2y)`


slope of the tangent `= dy / dx`


`1 = 1/(2y)`


`y=1 / 2`


`y^{2}=x`


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