#### Question

Find the points on the curve *y* = *x*^{3} at which the slope of the tangent is equal to the *y*-coordinate of the point.

#### Solution

The equation of the given curve is *y* = *x*^{3}.

`:. dy/dx = 3x^2`

The slope of the tangent at the point (*x*, *y*) is given by,

When the slope of the tangent is equal to the *y*-coordinate of the point, then *y* = 3*x*^{2}.

Also, we have *y* = *x*^{3}.

∴3*x*^{2} = *x*^{3}

⇒ *x*^{2} (*x* − 3) = 0

⇒ *x* = 0, *x* = 3

When *x* = 0, then *y* = 0 and when *x* = 3, then *y* = 3(3)^{2} = 27.

Hence, the required points are (0, 0) and (3, 27).

Is there an error in this question or solution?

Solution Find the Points on the Curve Y = X3 at Which the Slope of the Tangent is Equal to the Y-coordinate of the Point. Concept: Tangents and Normals.