For a cube whose edge length (in cm) varies with time (in s) according to

MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

For a cube whose edge length (in cm) varies with time

t

(in s) according to

a(t)=2t+t^{2}

, answer the following at

t=2\,\text{s}

: (i) Calculate

\dfrac{da}{dt}

. (ii) Hence find

\dfrac{dV}{dt}

. (iii) Determine the rate of change of the total surface area of the cube.