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Mathematics 71 Online
OpenStudy (anonymous):

Consider the problem of finding the square root of a number. There are many methods of computing square roots, and Newton's method is one. For example, if one wishes to find the square root of 612, this is equivalent to finding the solution to: x**2 = 612; The function to use is then: f(x) = x**2 - 612; with derivative, f'(x) = 2x... in this example, what does derivative mean and why is it 2x?

OpenStudy (anonymous):

\[f(x) = x ^{2} - 612, f'(x) = 2x\]

OpenStudy (anonymous):

derivative is the slope of the function f(x) at any particular value of x

OpenStudy (anonymous):

ah, they are still talking about line graphs... ok thanks

OpenStudy (anonymous):

http://en.wikipedia.org/wiki/Derivative

OpenStudy (anonymous):

it's a shame, I thought it was an example I could understand lol

OpenStudy (anonymous):

it means that at any instant, the fucntion f(x) changes at a rate of 2x.

OpenStudy (anonymous):

:) thankyou. How do you get such an answer? Make the graph, and figure out m? Nevermind, I'm only up to linear equations in my studies, my studies aimed at understanding newtons method for the purposes of programming, thought this was possibly a short-circuit to that understanding... but it is really the same...

OpenStudy (anonymous):

oh, might I ask if you are doing loops?

OpenStudy (anonymous):

or rather, iterations or recursive functions?

OpenStudy (anonymous):

the 2x is the slope of the function

OpenStudy (anonymous):

thry just want to know if you know the basics behind the method all it is is that you find an x value that is close to the x intercept of the graph ( ie the solution ) , then from that x co ordinate you go up to the function, draw a tangent line , and look at the x intercept of the line you just drew , and , hopefully ( unless you chose a point close to a turning point ) the next x intercept you get is a better approxiamtion to the solution

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