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

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

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 :

If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0) is equal to :