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The volume of a cube of edge x is increasing at a rate of 12 cm/s. Find the rate of change of edge of the cube when the edge is 6 cm.(a) \(\frac{1}{8}\)(b) \(\frac{2}{9}\)(c) –\(\frac{1}{9}\)(d) \(\frac{1}{9}\)The question was asked by my school principal while I was bunking the class.The question is from Derivatives Application topic in section Application of Derivatives of Mathematics – Class 12

Answer»

Right answer is (d) \(\frac{1}{9}\)

Explanation: Let the VOLUME of cube be V.

V=x^3

\(\frac{DV}{dt}\)=3x^2 \(\frac{DX}{dt}\)

12=3x^2 \(\frac{dx}{dt}\)

\(\frac{dx}{dt}=\frac{4}{x^2}\)

\(\frac{dx}{dt}\)|_x=6=\(\frac{4}{6^2}=\frac{4}{36}=\frac{1}{9}\).


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