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

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

Answers (1)

Answer:

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

Hint:

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

Given:

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

Solution:

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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