how does tangent lines play into this problem?
click here for problem
Do you understand that f(7) is the value of y when x=7?
yeah. i dont understand F'(7).
dy/dx = f'(x) is the slope of the curve y = f(x), so what is f'(7)?
am i supposed to plug 7 in for x and then take the derivative? how? doesn't the equation end up canceling out?
Why would you take the derivative?
The slope of the tangent line = the slope of the curve at the point where the line touches the curve.
oh, i didnt realize the d's stood for the difference.
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 lot harder!).
In the first place, the "d's" do not stand for difference!
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 not find the derivative of a function "when x= 7" by substituting 7 for x and then differntiating. The value of any function for a specific x is a number (a constant) and the derivative of a constant is always 0. Do it the other way around: first differentiate and then substitute.
so correct me if wrong. to find F(7), i just plug 7 for x in the equation of the tangent line and to find F'(7), I just differentiate the equation and then plug in 7 for x and solve for y?
I forget, what does differentiate mean?
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