Introducing 

Prezi AI.

Your new presentation assistant.

Refine, enhance, and tailor your content, source relevant images, and edit visuals quicker than ever before.

Loading…
Transcript

What is Calculus

Calculus Mind Map

  • CALCULUS is a tool used in mathematics to understand and predict how things change.

  • the formal study of Calculus has been credited to Sir Isaac Newton and Gottfried Wilhelm von Leibniz in the 17th century.

  • Fields such as physics, engineering, chemistry, economics, statistics and medicine have their roots in Calculus.

What is a Tangent?

  • A tangent is a line that most resembles the graph at a particular point.
  • In other words, it is the rate of change of the curve at a particular point.

Tangent Lines

Difference Quotient

In general, the slope of the tangent to the graph Y=f(X) at point P(a,f(a)) is this:

Topic

Rates of change

There are two types of rates of change on a given graph:

  • AROC
  • IROC

Topic

AROC

AROC stands for the average rate of change between two points on a graph

Topic

IROC

IROC stands for the rate of change at a specific point on a graph

Topic

What is a Derivative?

The derivative of a function is an equation used to find the slope of the function at any given point.

Derivatives

Topic

General Limit Equation

Limits

Properties of Limits

Topic

Continuous Graph:

Non-differentiable at the point of discontinuity

Topic

Discontinuous Graph:

The limit exists and is differentiable

Removable Discontinuity

Topic

Point Discontinuity

Topic

Jump Discontinuity

Topic

Infinite Discontinuity

Topic

Physics Application

Applications

  • The first derivative can be used to create a velocity function
  • The second derivative can be used to create the acceleration function

Velocity and Acceleration

Topic

Example Question

Topic

Maximum and Minimum Values

Max and Min values are also called extreme values or "absolute extrema"

Max and Min

Example Question

Topic

Optimization Problems

Omptimization

  • In and optimization problem, you must determine the maximum or minimum value of a quantity.
  • It can be used in real-world situations such calculating max profit with respect to cost and price.

Steps for a optimization Problems:

Topic

1. Draw and label a diagram, If possible

2. Define variable & identity domain (restrictions)

3. Determine a function in one variable that represents the quantity being optimized

4. Differentiate to locate extrema values and compare endpoints (where applicable)

Example Question

Topic

Learn more about creating dynamic, engaging presentations with Prezi