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Optimization is required in situations that frequently arise in finance and other areas. Organizations would like to maximize their profits or minimize their costs at a given level of output. An individual would like to maximize his utility when choosing investment alternatives. If we have a mathematical function, then we can find a solution to the optimization problem using calculus.
Of all the higher order derivatives, the second order derivative is of special interest in problems of optimization.
The first derivative of a function, f'x is the slope of the function f(x), or the rate of change in the value of f(x) per unit change in x. Similarly the second derivative, f''x is the slope of the function f'x or the rate of change in the value of f'x per unit change in x, which is the rate of change of the original function f(x).
The following figures and table show various combinations of signs of f'x and f''x and the implied slope of the graph of f(x).
f'x
f''x
f(x) is
positive
increasing at an increasing rate
negative
increasing at a decreasing rate
decreasing at an increasing rate
decreasing at a decreasing rate
A toy company produces 2 models of water guns: spray king and zapper. They are manufactured in batches for easier packaging and sale. Two of the limiting resources are 1200 pounds
log6 X + log6 (x-5) = 1
4 7 9 6
13 1/4 34 56/89
Parallel Vectors - Applications of Scalar Multiplication This is an idea that we will see fairly a bit over the next couple of sections. Two vectors are parallel if they have
850ml is to be administered to a person over 8 hours using a drop factor of 20 drops/ml what is the flow rate in gtts/min ?
5to6
I would like to know what a symbol in my homework means?
#question.how to creat table
Explain Analytical Models in Operations Research with Application
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