5
Malak Noufal 12G4
Applications OF DERIVATIVES
DEFINITION
DEFINITION
The derivative is the exact rate at which one quantity changed with respect to another. In calculus, we have learned that when y is the function of x, the derivative of y with respect to x measures the rate of change in y with respect to x. Geometrically, the derivatives are the slope of the curve at a point on the curve.
OBJECTIVES
The objectives of this project is to gain information into how and why calculus is important for our life and this power-point will be focusing on derivatives.
in physics
IN
physics
Derivatives with respect to time
In physics, we are often looking at how things change over time
1. Velocity is the derivative of position or 1st derivative
2. Acceleration is the derivative of velocity or 2nd derivative
DAILY LIFE !GAMES!
DAILY
LIFE Example
IF YOU DON’T UNDERSTAND DERIVATIVES, YOULL SUCK AT MANY GAMES
Say you're playing a game, when you shoot a moving enemy, it is very easy to miss. So you need to predict where they might be in the next moment, and then shoot there. That’s how you get them.
HOW YOU predict
HOW YOU
predict
You predict by checking out the direction and speed of their movement, i.e. the derivative of their movement. Then when you predict their eventual location, you are unintentionally doing a mental integration. That’s how you predict their movement and get your shot.
Say you play another game. Do you spend you real life dollars to buy in game golds, or do you add another builder
I say you should add another builder because that increases the derivative of your gold quantity.
In short, any game with changing numbers, be it victory points, scores, or in game money, or level of experience, must uses derivatives somehow.
So derivatives can help you understand or invent strategies to crash people who naively think that math is useless.