Definitions+and+Theorems

toc =Definition of a Limit= =Definition of Continuity= == =Intermediate Value Theorem=

Chain Rule: f(x) = g(h(x))
**f '(x) = g '(h(x)) x h '(x)**

Product Rule: f(x) = g(x)h(x)
**f '(x) = g(x)h '(x) + g '(x)h(x)**

Quotient Rule: f(x) = g(x) / h(x)
**f '(x) = (h(x)g '(x) - g(x)h '(x)) / (h(x))^2**

= Definition of Critical Points: =

=Definition of a Point of Inflection:=

=Mean Value Theorem= = = =Rolle's Theorem= Rolle's Theorem, named after Michel Rolle (1652-1719) states that : If f is continuous on [a,b] and differentiable on (a,b) AND if f(a) = f(b) = 0, then there is at least one number x = c in (a,b) such that f '(c) = 0. This is a special case of the Mean Value Theorem guaranteeing, if f is continuous and differentiable on the appropriate intervals, the existence of a local extrema for an x value between a and b if f(a) and f (b) are both zero.