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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, b,c are in h.p prove that a/b+c-a, b/a+c-b, c/a+b-c are in h.p To prove: (b+c-a)/a; (a+c-b)/b; (a+b-c)/c are in A.P or (b+c)/a; (a+c)/b; (a+b)/c are in A.P or 1/a; 1
If the normal to y=f(x) makes an angle of pie/4 with y-axis at (1,1) , then f''(x) is eqivalent to? Ans) The normal makes an angle 135 degree with the x axis. also f ''(1)
assinment
how to divide an arc in three equal parts
Seth has a pet goldfish. When he got his goldfish , it was only 5 centimeters long . Now it has grown to be 92 millimeters long. How many millimeters has the goldfish grown since
In a class,there are 174 students in form three,86 students play table tennis,84 play football and 94 play volleyball,30 play table tennis and volleyball,34 play volleyball and foo
how do we figure it out here is an example 3,4,6,9,_,_,_,_,_,. please help
Evaluate: 30 - 12÷3×2 =
Rank Correlation Coefficient Also identified as the spearman rank correlation coefficient, its reasons is to establish whether there is any form of association among two vari
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