Review Definitions AP Calc

Highschool Class

Definition of Continuity at a point

Removable Discontinuity

Holes

Infinite Discontinuity

Asymptote

Bigger On Bottom

Zero

Conditions of the IVT

1. f(x) is continuous on [a,b]

2. d is between f(a) and f(b)

Conclusion of IVT

There exists a value c such that f(c ) = d.

f’(a) as a limit of a difference quotient

L’Hopital’s Rule

If both the bottom and the top are 0 or ♾, then take the derivative of both. This new equation is equal to the original.

Conditions of MVT

f is differentiable on (a,b) and continuous on [a,b]

Conclusion of MVT

There exists a c in (a,b) such that

Conditions of EVT

f is continuous on [a,b]

Conclusion of EVT

f(x) must have a maximum & minimum value on [a,b]

Rules for concavity

1. f’’(x) > 0

   or

2. f’(x) is increasing on the interval

Definition of a Critical Value

A value, c, in domain of f such that: f’(c ) = 0 or f’(c ) is undefined

Point of Inflection (using f’(c ))

If f’(c ) changes from increasing to decreasing or decreasing to increasing at x = c

Point of Inflection (using f’’(c ))

If f’’(c ) changes from positive to negative or negative to positive at x = c