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

Question

Philoid · Accepted Answer

Given:

The curve is y = x²

Differentiating the above w.r.t x

⇒ y = x²

⇒ = 2x^{2 – 1}

⇒ = 2x ...(1)

= The Slope of the tangent = tan

Since, the tangent make an angle of 45^o with x – axis

i.e,

⇒ = tan(45°) = 1 ...(2)

tan(45°) = 1

From (1) & (2), we get,

⇒ 2x = 1

⇒ x =

Substituting x = in y = x², we get,

⇒ y = ()²

⇒ y =

Thus, the required point is (,)