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Calculus in 10 Minutes or Less
Slope
position
time
Slope
position
time
tangent!
Derivatives
Derivatives are the slope of a function at a point Slope of x vs. t
velocity - describes how position changes over time Slope of v vs. t
acceleration - describes how velocity changes over time
Slope of a vs. t jerk - describes how acceleration changes over time
Derivatives
Derivative Rules
If the position of an object is described by the function
What are the velocity and acceleration functions?
Area
velocity
time
Easy!
Area
velocity
time
Harder!!!
Integrals
Integrals are anti-derivatives Graphically, integrals are the area
under a curve Area under a v vs. t graph = Displacement
Integrals
Integral Rules
An object’s acceleration is described by a(t) = 2t. Find the velocity and position functions.
Initial ConditionsIf x = 5 when t = 0, what is the displacement function for this velocity function?
-so- -so-
Definite Integrals
Taking the integral from one point to another.
Same rules apply, but don’t have to do “+C”
Find the displacement from t = 2 seconds to t = 4 seconds for the velocity function
