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Home » A particle moves along the curve y = x3. Find the points on the curve at which the y – coordinate changes three times more rapidly than the x – coordinate.
A particle moves along the curve y = x3. Find the points on the curve at which the y – coordinate changes three times more rapidly than the x – coordinate.
CBSE | Class 12 | Derivatives as a Rate Measurer | Exercise 13.2 | Maths | RD Sharma
A particle moves along the curve y = x3. Find the points on the curve at which the y – coordinate changes three times more rapidly than the x – coordinate.

According to question,

a particle moves along the curve

    \[y\text{ }=\text{ }{{x}^{3}}.\]

To find the points on the curve at which the y – coordinate changes three times more rapidly than the x – coordinate

Equation of curve is 

    \[y\text{ }=\text{ }{{x}^{3}}.\]

Differentiating the above equation with respect to t, we get

RD Sharma Solutions for Class 12 Maths Chapter 13 Derivative as a Rate Measurer Image 36

When

    \[x\text{ }=\text{ }1,\text{ }y\text{ }=\text{ }{{x}^{3}}~=\text{ }{{\left( 1 \right)}^{3}}\Rightarrow ~y\text{ }=\text{ }1\]

When

    \[x\text{ }=\text{ }\text{ }1,\text{ }y\text{ }=\text{ }{{x}^{3}}~=\text{ }{{\left( -\text{ }1 \right)}^{3}}\Rightarrow ~y\text{ }=\text{ }\text{ }1\]

Hence the points on the curve at which the y – coordinate changes three times more rapidly than the x – coordinate are (1, 1) and ( – 1, – 1).

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