Absolute extreme values of f(x)= \left| x \right| , \quad-1 < x < 2  are _____________ and _____________.

If  u = x + y and v = x - 2y  then   \frac{\partial(u,v)}{\partial(x,y)} is _______________.

Suppose that f '(x) = 2x for all x. Find f(2) if f(1) = 0. [Hint: Use Mean Value Theorem]

The absolute maximum and minimum values of the function y = x^4 \; in \;(- \infty, \infty ) are respectively ______________ and ______________.

The absolute maximum and minimum values of the function f(x) = \sqrt{4 - x^2}, \quad -2 \leq x \leq 1 are _________ and _________.

The number of independent variables in an implicit function is ____________.

The function f(r) = 3r^3 + 16r is _____________.

If a function is continuous at a point, then its limit exists at that point.

The critical points of the function f(x) = \frac{x^2(x - 1)}{x + 3}, \quad x \ne -3 are ________________.