Hi, I'm doing an assignment on real life applications of differentiation. Any examples?

Answer 1

Velocity of an aircraft, sending up satellites, rate of population growth, deriving the probability density function of a continuous random variable, etc.

Answer 2

The best example is optimization which is used in business all the time, the problem usually consist of some sort of formula which would involve you finding the value of x, finding the derivative to set it equal to zero in order to find the relative maximum, then evaluate your results...
Heres a good sample problem i found on the net involving apple production...
PROBLEM: There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additional tree planted in the orchard, the output per tree drops by 10 apples. How many trees should be added to the existing orchard in order to maximize the total output of trees ?
SOLUTION : Let variable x be the ADDITIONAL trees planted in the existing orchard. We wish to MAXIMIZE the total PRODUCTION of apples

P = (number of trees) (apple output per tree)

= ( 50 + x ) ( 800 - 10x )

= 40,000 + 300 x - 10 x2 .

Now differentiate this equation, getting

P' = 300 - 20 x

= 20 ( 15 - x )

= 0

for

x=15 .

See the adjoining sign chart for P' .



If

x = 15 additional trees ,

then

P = 42,250 apples

is the largest possible production of apples.

Answer 3

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Answer 4

Yes, maximisation and minimisation problems, also related rate of change problems.
The ones in textbooks are always pretty contrived though and don't seem that realistic.

Have to admit I've never personally used it in real life!