Principles of Calculus

Derivative - A derivative of a function is a new function that shows the slope of the tangent at that point for the original function. example - Velocity in a distance /time graph

Rules to differentiate

First derivative test - Is done to check if the function has reached local maximum or local minimum when f'(x) changes from positive to negative or the other way around to show that slope of tangent has changed. this helps to graph the function

Point of inflection - A point in function where f''(x) = 0 or does not exist. this shows when a graph is switching from concave up to concave down.

Derivative of exponential and trigonometric functions

Tangent - Instantaneous ROC

Secant - Average ROC

Definition of Limit - the value of a function as it is approaching a point (a) left side and right side limits can be used to figure out if a function has discontinuities.

Second derivative - is a new function that shows the slope of the tangent at that point for the first derivative function. example - Acceleration is Distance / Time graph

Critical point - A point in function where F'(x)= 0 or does not exist. This is helpful because it shows maximum and minimum points on a function. (also local maxima and minimum)