Derivatives (12 videos)

Growth Rate and Log Graphs

It is good to know how fast different functions grow.  Professor Strang puts them in order from slow to fast:
    logarithm of x    powers of x    exponential of x     x factorial    x to the x power   What is even faster??

And it is good to know how graphs can show the key numbers in the growth rate of a function
A LOG-LOG graph plots log y against log x   If y = A x^n then log y = log A + n log x == LINE WITH SLOPE n

A SEMILOG graph plots log y against x        If y = A 10^cx then log y = log A + cx == LINE WITH SLOPE c
You will never see y = 0 on these graphs because log 0 is minus infinity.  But n and c jump out clearly.

Professor Strang’s Calculus textbook (1st edition, 1991) is freely available here .

Subtitles are provided through the generous assistance of Jimmy Ren.

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