AI

Artificial Intelliegence & Derivatives

Presented by: Moza Al Falasi 12-BG

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1.

Introduction to AI

What is Artificial Intellegience & Why is it Important?

Artificial intelligence (AI) refers to the simulation of human intelligence in machines that are programmed to think like humans and mimic their actions.AI technology is important because it enables human capabilities – understanding, reasoning, planning, communication and perception – to be undertaken by software increasingly effectively, efficiently and at low cost.

Examples of AI

Uses of AI

Digital AssistantsChatbots E-Payemnts Google `Maps

Writing, speech, and voice recognition. Solving math problems.

What is a derivative?

The rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.

Real-world Scenarios where we would use derivatives

Checking tempretaure variation

Calculating the profit and loss in business using graphs

Deriving equations in physics

Determining the speed or distance covered such as miles per hour

Steps to find derivative of a function

The derivative of f(x) can be computed using the limit definition of derivatives with the following steps:

4. Take the limit, as h approaches 0, of the simplified difference quotient.

3. Simplify the difference quotient.

2. Plug f(x + h), f(x), and h into the limit definition of a derivative.

1. Find f(x + h).

How can the steps of a derivative be expressed in a formula?

Basic Derivatives Rules

Quotient Rule

Chain Rule

Constant rule

Constant Multiple rule

Power Rule

Sum/differnce Rule

Lagrange's notation

In Lagrange's notation, the derivative of f is expressed as f'.

Different Ways to Express a Derivative

Leibniz's notation

In, Leibniz's notation, derivative of f is expressed as d/dx f(x).

Derivatives are expressed mathematically in derivative notation.

Newton's notation

In Newton's notation, the derivative of f is expressed as f˙and the derivative of y=f(x) is expressed as y˙.

Real Life Applictaion of Derivatives

1.C(x)=(10^-6)x^3-0.003x^2+5x+1000 C'(x)=3(10^-6)x^2-0.006x+5 C''(x)=6(10^-6)-0.006 2.

Suppose that the cost function for a company to produce its products is given by the function:C(x)=(10^-6)x^3-0.003x^2+5x+1000 dollars 1. Find the derivative of cost function. 2. Graph C(x) & C'(x)

Using Artificial Intelligence to minimixe and maximize my output

By using AI, it can read through the information and tell me when there are a lot of products selling so the profit will reach its maximum point. AI can inform when the demand is less and when can I expect my profit to reach its minimum point. Machine learning can also use algorithims to help minimize and maximize my output,