Question

Find a point on the curve y = x2 where the slope of the tangent is equal to the x – coordinate of the point.

Answer 1

Given as the curve is y = x2

y = x2

Differentiate the above with respect to x

(dy/dx)= 2x2 - 1

(dy/dx)= 2x ...(1)

The slope of tangent is equal to the x-coordinate,

(dy/dx)= x ...(2)

From the equation (1) & (2),

2x = x

⇒ x = 0.

Substitute in y = x2,

y = 02

⇒ y = 0

Hence, the required point is (0, 0)