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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 right triangle whose sides are 15 cm and 20 cm is made to revolve about its hypotenuse. Find the volume and surface area of the double cone so formed. (Ans : 3768cu.cm,1318.8
Basic indefinite integrals The first integral which we'll look at is the integral of a power of x. ∫x n dx = (x n +1 / n + 1)+ c, n
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y=log4(x). i am unsure what this graph is supposed to look like?
$112 in 8 hours
Divergence Test Once again, do NOT misuse this test. This test only says that a series is definite to diverge if the series terms do not go to zero in the limit. If the
A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.
The lower portion of a hay stack is an inverted cone frustum and the upper part is a cone find the total volume of the hay stack.
1. Using suffix trees, give an algorithm to find a longest common substring shared among three input strings: s 1 of length n 1 , s 2 of length n 2 and s 3 of length n 3 .
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