why we take derivative of the function?

- anonymous

why we take derivative of the function?

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- schrodinger

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- .Sam.

There's a LOT of things you can do with derivative,
http://en.wikipedia.org/wiki/Derivative

- anonymous

any example?

- .Sam.

Inflection point

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## More answers

- anonymous

well i am jst asking what is its use in our daily life?

- Callisto

finding that rate of change... for example, the velocity of a car can be found by ds/dt

- .Sam.

yes

- .Sam.

Lets say if you were to build a square fence and wanted to use the least amount of fencing possible to make that fence of 1000 square feet,then the derivative can be helpful

- anonymous

how?

- anonymous

you can use calculus to work out the closest distance between moving objects

- .Sam.

Example
Find dimensions of recangle of area 1000, whose peimeter is small as possible,
|dw:1333189696727:dw|
Minimum perimeter: P=2x+2y
Area,A=xy,
y=1000/x
P=2x+1600/x
Derivative of P, 2-2000/x^2
2-2000/x^2=0
x^2=1000
x=sqrt(1000)

- .Sam.

my comp crashed just now ,lol

- anonymous

we have boat A and boat B , and at time = 0 they have positions (2i + j) and (-i + 2j) respectively, where i and j are unit vectors pointing east and north respectively.
boat A travels with constant velocity (-i + j) and boat B travels with constant velocity
(3i + 0j)
using equation speed = distance/ time
at time t:
\[Ra = (2 - t)i + (1 + t)j \] -position of A
\[Rb = (-1 + 3t)i + 2j \] -position of B
the position of A relative to B is Ra - Rb :
\[Rab = (3 -4t)i + (-1 +t)j\]
now find the distance between using Pythagoras on the vector.
\[|Rab| =\sqrt{(3-4t)^2 + (t-1)^2 }\]
\[|Rab| = \sqrt{(9-24t +16t^2) + (t^2 -2t +1)}\]\[|Rab|^2 = 17t^2 -26t + 10\]
let \[|Rab| = f(x)\]
now \[f'(x) = 34t -26\]
so there is a maximum at \[t= 26/34 = 13/17\]
substituting this into |Rab| gives us the min distance

- anonymous

situations in everyday phenomena can/are modeled by functions... you might want to know when is the best time to sell a stock...(max/min problem)

- anonymous

it really depends on how you define "our daily life" , if you're an engineer your daily life will depend more on knowing calculus than if you're selling fast food

- anonymous

Here is my answer... it is copied from this website.
(http://www.essortment.com/math-basics-calculus-used-for-60928.html)
"Credit card companies use calculus to set the minimum payments due on credit card statements at the exact time the statement is processed by considering multiple variables such as changing interest rates and a fluctuating available balance.
Biologists use differential calculus to determine the exact rate of growth in a bacterial culture when different variables such as temperature and food source are changed. This research can help increase the rate of growth of necessary bacteria, or decrease the rate of growth for harmful and potentially threatening bacteria.
An electrical engineer uses integration to determine the exact length of power cable needed to connect two substations that are miles apart. Because the cable is hung from poles, it is constantly curving. Calculus allows a precise figure to be determined.
An architect will use integration to determine the amount of materials necessary to construct a curved dome over a new sports arena, as well as calculate the weight of that dome and determine the type of support structure required.
Space flight engineers frequently use calculus when planning lengthy missions. To launch an exploratory probe, they must consider the different orbiting velocities of the Earth and the planet the probe is targeted for, as well as other gravitational influences like the sun and the moon. Calculus allows each of those variables to be accurately taken into account.
Statisticians will use calculus to evaluate survey data to help develop business plans for different companies. Because a survey involves many different questions with a range of possible answers, calculus allows a more accurate prediction for appropriate action.
A physicist uses calculus to find the center of mass of a sports utility vehicle to design appropriate safety features that must adhere to federal specifications on different road surfaces and at different speeds.
An operations research analyst will use calculus when observing different processes at a manufacturing corporation. By considering the value of different variables, they can help a company improve operating efficiency, increase production, and raise profits.
A graphics artist uses calculus to determine how different three-dimensional models will behave when subjected to rapidly changing conditions. This can create a realistic environment for movies or video games.
Obviously, a wide variety of careers regularly use calculus. Universities, the military, government agencies, airlines, entertainment studios, software companies, and construction companies are only a few employers who seek individuals with a solid knowledge of calculus. Even doctors and lawyers use calculus to help build the discipline necessary for solving complex problems, such as diagnosing patients or planning a prosecution case. Despite its mystique as a more complex branch of mathematics, calculus touches our lives each day, in ways too numerous to calculate."

- anonymous

mistake, i should have let \[f(x) = |Rab|^2\]

- kunal

we generally take a derivative to know the minimum/maximum value of a function.......
put f'(x)=0 for a function in variable x and this will give us the min/max. value of that function

- anonymous

duuuuh, should be f(t)

- anonymous

i fail

- saifoo.khan

To find it's change.

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