For the function below, find

f(x)= 12x^3 -9x^2-108x +4

a. the critical numbers.
b. the open intervals where the function is increasing.
c. the open intervals where it is decreasing.

For which rational expression is -2 an excluded value of x?

To find the extreme values of a function f(x.y) on a curve x-x(t), y y(t), treat f as a function of the single variable t and use the chain rule to find where df/dt is zero. in any other single-variable case, the extreme values of f are then found among the values at the critical points (points where df/dt is zero or fails to exist), and endpoints of the parameter domain. find the absolute maximum and minimum values of the following function on the given curves. use the parametric equations x=2cos t, y 2 sin t functions: curves: i) the semicircle x4,y20 i) the quarter circle x2+y-4, x20, y20 b, g(x,y)=xy

Simplify the expression and find the missing terms. the simplest form of has in the numerator and in the denominator.