So, what is your pick?

In optimization problem, we are always asked to find the value that will minimize/maximize.

Below are some tips in solving optimization problems which I found it quite useful:

• 1. Read each problem slowly and carefully. Read the problem at least three times before trying to solve it. Sometimes words can be ambiguous. It is imperative to know exactly what the problem is asking. If you misread the problem or hurry through it, you have NO chance of solving it correctly.




• 2. If appropriate, draw a sketch or diagram of the problem to be solved. Pictures are a great help in organizing and sorting out your thoughts.




• 3. Define variables to be used and carefully label your picture or diagram with these variables. This step is very important because it leads directly or indirectly to the creation of mathematical equations.




• 4. Write down all equations which are related to your problem or diagram. Clearly denote that equation which you are asked to maximize or minimize. Experience will show you that MOST optimization problems will begin with two equations. One equation is a “constraint” equation and the other is the “optimization” equation. The “constraint” equation is used to solve for one of the variables. This is then substituted into the “optimization” equation before differentiation occurs. Some problems may have NO constraint equation. Some problems may have two or more constraint equations.




• 5. Before differentiating, make sure that the optimization equation is a function of only one variable. Then differentiate using the well-known rules of differentiation.




• 6. Verify that your result is a maximum or minimum value using the first or second derivative test for extrema.

These tips are extracted from http://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/maxmindirectory/MaxMin.html. There are also a few examples given in the link.

Do check it out!

More often than not, I need to apply change of base formula in the field of Digital Logic Design.

The change of base formula is as follow:

log_bx = log_ax / log_ab

where / denotes divide, and a = any integer for the base

on my dual-monitor set up:

Brillant, isn’t it?

Extracted from: http://www.wretch.cc/blog/cwwany/26692785

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Q1: y = ln(2x)

d/dx [(ln(2x)] = 1/2x . 2
= 1/x

Q2: y = ln(x)^2

d/dx [ln(x)^2] = 1/x^2 . 2x
= 2/x

Alternatively, ln(x)^2 = 2 . ln(x)

d/dx [2 . ln(x)] = 1/x . 2
= 2/x

Q3: y = ln(4x^2)

d/dx [ln(4x^2)] = 1/4x^2 . 8x
= 2/x