# 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:**

For a curve y = f(x) containing the point (x_{1},y_{1}) the equation of the tangent line to the curve at (x_{1},y_{1}) is given by

y − y_{1} = f′(x_{1}) (x − x_{1})

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

Therefore,

dy/dx= 3x^{2}

When the slope of the tangent is equal to the y-coordinate of the point,

then according to the question,

y = 3x^{2}

Also, we have y = x^{3}

Therefore,

3x^{2} = x^{3}

⇒ x^{2} (x - 3) = 0

⇒ x = 0, x = 3

When, x = 0,

⇒ y = 3 and x = 3,

⇒ y = 3(3)^{2} = 27

Thus, the points are (0, 0) and (3, 27)

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.3 Question 17

## 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

**Summary:**

The points on the curve y = x^{3 }at which the slope of the tangent is equal to the y-coordinate of the point are (0, 0) and (3, 27)