CBSE (Commerce) Class 12CBSE
Share
Notifications

View all notifications

Find the Points on the Curve Y = X3 at Which the Slope of the Tangent is Equal to the Y-coordinate of the Point. - CBSE (Commerce) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

Find the points on the curve y = x3 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 = x3.

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

The slope of the tangent at the point (xy) is given by,

When the slope of the tangent is equal to the y-coordinate of the point, then y = 3x2.

Also, we have y = x3.

∴3x2 = x3

⇒ x2 (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?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 12 (2018 to Current)
Chapter 6: Application of Derivatives
Q: 17 | Page no. 212
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.
S
View in app×