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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 polynomial satisfies the following relation f(x).f(1/x)= f(x)+f(1/x). f(2) = 33. fIND f(3) Ans) The required polynomial is x^5 +1. This polynomial satisfies the condition state
Which of the subsequent numbers is equivalent to 12.087? Zeros can be added to the end (right) of the decimal portion of a number without changing the value of the number; 12.
Limits At Infinity, Part I : In the earlier section we saw limits which were infinity and now it's time to take a look at limits at infinity. Through limits at infinity we mean
Let a 0 , a 1 ::: be the series recursively defined by a 0 = 1, and an = 3 + a n-1 for n ≥ 1. (a) Compute a 1 , a 2 , a 3 and a 4 . (b) Compute a formula for an, n ≥ 0.
Explain Coin Problem? How to resolve Coin Problem? Explain brief...
a. Cassie has seven skirts, five blouses, and ten pairs of shoes. How many possible outfits can she wear? b. Cassie decides that four of her skirts should not be worn to school.
The form x2 - bx + c ? This tutorial will help you factor quadratics that look something like this: x 2 -7x + 12 (No leading coefficient; negative middle coefficient; p
How do you solve (17+w)^2 + w^2 = (25+w)^2
cos 8
how to solve this? y = 7x - 12 y = x2 Solve the system using substitution.
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