Chapter 4 Calculus Theorems

Squeeze Theorum : If for all x f(x) is less then or equal to g(x) less than or equal to h(x) and large If f(x) => L and h(x) => L then g(x) =>L

Intermediate Value Theorum : The continuous function f on interval [a,b] takes on all range values between f(a) and f(b) at least once for domains between a and b

First Derivative Test : Identifies where critical points occur

Second derivative Test : Identifies whether critical point is concave up,down, or has a terrace point

Definition of limit at a point : For every positive number espelon there is a positive number delta such that |f(x)-L|<espelon for all x such that 0<|x-a|<delta. then lim as x->a=L

Definition of continuity of a function at a point : Let f be a function defined on an interval I, containing x=a. If lim f(x) as x approaches a from the left and right side, is equal to f(a), then the function is continuous at the point, x=a