If the surface area of a cube is increasing at a rate of 3.6 cm²/sec, retaining its shape; then the rate of change of its volume (in cm³/sec), when the length of a side of the cube is 10 cm, is :

The function, f(x) = (3x – 7)x^2/3, x $$ \in $$ R, is increasing for all x lying in :

Let f : (–1, $$\infty $$) $$ \to $$ R be defined by f(0) = 1 and
f(x) = $${1 \over x}{\log _e}\left( {1 + x} \right)$$, x $$ \ne $$ 0. Then the function f :

The equation of the normal to the curve
y = (1+x)^2y + cos ²(sin^–1x) at x = 0 is :