Question

Find the points on the curve y=x³ at which the slope of tangent is equal to the y co-ordinate of the point.

Answer 1

Answer:

Heya mate here is your answer is in image :

Answer 2

Answer:

let the point be (h,k) on the plane

when slope of tangent at (h,k) = y coordinate of (h,k)

that is dy/dx (h, k) = k

Given y = x ³

Differentiating with respect to x, then

dy/dx = 3x²

Hence, slope of tangent at (h, k) is

dy/dx(h, k) = 3h²