calculus in 10 minutes or less

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