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1> EXAMPLE
.
A>A speed limit is an example of a
real world limit. If the speed limit is
45 mph a car may not exceed 45 mph
without getting a ticket.
1
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2ND EXAMPLE !!
2> When you go to the grocery store and there
is a purchase limit on a special of a product. A
consumer may only purchase up to that certain
amount.
5. 3RD EXAMPLE
C>If you go to the amusement park and there
may be a weight limit on a ride. Any person can
ride the ride as long as they do not weigh more
than that weight.
-Continuity is a period of consistency.
=A limit is trying to reach continuity.
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DERIVATIVES
DEFINITION: A derivative is something that is created
from something else, not original.
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EXAMPLE 1
An apple company producing new apple iPhone 7 & a Chinese company
comes in with the exact copy which is pretty much made in china & also
has a cheap price range then the actual original iPhone 7 so the Chinese
company derived the phone and copied and tried to make similar product.
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EXAMPLE 2
Suppose a loaf of bread sliced into 10 pieces. You are asked to eat it one by one. I'm
watching you while you are eating.
I found that you are eating 1 bread per minute. Then at the end (after 10 minute). I can
say that you’re eating speed is 1 bread / minute.
In real life terms example as shown below the sudden direction of the change is the
main motive of knowing the derivative so derivative will have full meaning.
For example:
y = x^3
dy/dx= 3x^2
y''' = 6
Here 6 is constant form.
6x is finite in constant multiplied
3x^2 is little complex, having many finite parts
x^3 is more complex.
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EXAMPLE 3
ICE CREAMMILK
MOO
COW
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THE REAL DEAL
(HOW IT WORKS)
If you run a business (say selling ice creams), derivatives can help you decide what
quantity you should sell.
Your manager gives you some data how your business has been performing over the
past few months. You tabulate the data and draw a curve to see the trend.
You sell each ice cream for 10 bucks.
x-axis shows the number of units you produced
y-axis shows the cost you incurred
(there is some fixed cost, as seen when units produced=0)
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WHAAAAAAAAAAAAT!!!!
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PAY ATTENTION !!!
• You seem impressed with the 'growth' shown in the graph. However, you are curious why
the curve is getting steeper as the quantity increases. Your manager tells you that since
for producing more ice cream you need more milk, he reaches out to milk sellers in other
areas of the city to provide milk. So the transportation
• you seem impressed with the 'growth' shown in the graph. However, you are curious why
the curve is getting steeper as the quantity increases. Your manager tells you that since
for producing more ice cream you need more milk, he reaches out to milk sellers in other
areas of the city to provide milk. So the transportation cost increases, hence the steepness
in the curve.
• At this moment you can feel happy that your product is in demand and that your business
is growing!
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THIS IS HOW ITS DONE LIKE A BOSS!!
• Enter the Derivative"
• Now, derivative can tell you the instantaneous slope (dy/dx) of this graph. Slope tells you the
marginal cost (change in cost/change in unit produced) of producing every additional unit at that
instant. If this cost is more than 10 bucks (your selling price), you are making a loss at that point!
• For a simpler understanding, refer to the table given alongside.
• From 0-200 units, your cost > sales, you are making a loss
• From 300-800 units, your sales > cost, you are making a profit :)
• From 900-1000 units, your cost > sales, you are again making a loss again! (and you thought you
were selling more and your business was growing ?)
• Derivatives just made you take a call on the number of ice creams you should make.
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ENJOY THE ICE CREAM
