Calculus 1 Vocab - Chapter 3

Relative Maximum (minimum)

a point on the graph where it’s at its max/min in that neighborhood

Absolute Maximum (minimum)

a point on the graph where it’s at an overall max/min

Critical points

a point on the graph where the derivative is either zero or undefined

Increasing function

The graph increases as you move right, f’(x) > 0

Decreasing function

The graph decreases as you move right, f’(x) < 0

Rolle’s Theorem

Function f is continuous on the closed interval [a, b] and is differentiable in its interior (a, b). If f(a) = f(b), then there exists some number c in (a, b) such that the derivative, f ‘(c), equals the slope between the two points.

Mean Value Theorem

1. 1. if f is continuous for all x values in [a, b]

2. 2. if f is differentiable in (a, b), then f’(c) = (f(b) - (a))/b-a (the derivative, f ‘(c), equals the

   slope between the two points) where c is between a and b

Concave Upward

A region on the graph where the curve opens up, f ”(x) > 0

Concave Downward

A region on the graph where the curve opens down, f ‘(x) < 0

Point of Inflection

A point where a graph changes from concave up to concave down or vice versa. f ”(x) = 0 or f ”(x) is undefined

Reciprocals of Zero and Infinity

1/0 → ∞ , 1/∞ → 0 and 1/-∞ → 0