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Please Solve RD Sharma Class 12 Chapter15 Tangents and Normals Exercise Fill in the blanks Question 16 Maths Textbook Solution.

Answers (1)


      Points are \left ( 0,0 \right )  and  \left ( 3,27 \right )


If the slope of tangent is equal to ordinate of point that means  \frac{dy}{dx}=y


The slope of tangent to curve  y=x^{3}  at a point is equal to ordinate of point.

To find:

We have to find the point


We have,

                y=x^{3}                                                                                                                                                … (i)

On differentiating with respect to x , we get

\frac{dy}{dx}=3x^{2}                                                                                                                  \left[\because \frac{d\left(x^{n}\right)}{d x}=n x^{n-1}\right]

Now, we know that the given slope of tangent to the given curve at a point is equal to ordinate of point

3x^{2}=y                                                                                                                                               … (ii)

Putting value of  y in equation (i), we get

\Rightarrow         3x^{2}=x^{3}

\Rightarrow     x=3,0  and  y= 0,27   [From equation (i)]

Thus the two points are  \left ( 0,0 \right ) and \left ( 3,27 \right )

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