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how does tangent lines play into this problem?

http://www.eden.rutgers.edu/~cjjacob/images/calc.jpg [Broken]

http://www.eden.rutgers.edu/~cjjacob/images/calc.jpg [Broken]

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- Thread starter ACLerok
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- #1

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http://www.eden.rutgers.edu/~cjjacob/images/calc.jpg [Broken]

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- #2

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Do you understand that f(7) is the value of y when x=7?

- #3

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yeah. i dont understand F'(7).

- #4

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dy/dx = f'(x) is the slope of the curve y = f(x), so what is f'(7)?

- #5

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- #6

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The slope of the tangent line = the slope of the curve at the point where the line touches the curve.

- #7

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so to find F(7), I isolate y on one side of the equation and then plugin 7 for x and solve for y? what do i do for the F'(7)? slope of the line when x=7?

- #8

HallsofIvy

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Originally posted by ACLerok

so to find F(7), I isolate y on one side of the equation and then plugin 7 for x and solve for y? what do i do for the F'(7)? slope of the line when x=7?

These are all things that should be elementary (believe me, the problems are going to get a

In the first place, the "d's" do

They are simply the notation for derivative. Yes, one method of finding the derivative of a function is to take the limit of the "difference quotient" but I don't think you should think "the d's stand for the difference".

In any case, the first thing you should have learned about the derivative of a function is that "the derivative IS the slope of the tangent line".

In this case, yes, solve for y. The value of y when x= 7 is the value of the function F when x= 7, F(7). The slope of that line is the derivative of F when x= 7 dF/dx(7) or F'(7).

By the way, you do

- #9

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I forget, what does differentiate mean?

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