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Math Help - Derivates for equation of tangent and normal

  1. #1
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    Derivates for equation of tangent and normal

    If f(2)= 3 and f'(2)= 5, find an equation (a) the tangent line, and (b) the normal line to the graph of y=f(x) at the point where x=2.

    Guess:
    f(2)=3 refers to the answer of a basic derivative ( lim as h--> 0 \frac {f(x-h) -f(x)}{h} )of an unknown equation with x=2.

    f'(2)=5 refers to the answer of the same equation in the other definition
    lim as x--> a \frac {f(x)-f(a)}{x-a} with x=2.

    Either that f(2) in some equation of the derivative = 3 and 5.
    I'm inclined to believe the latter.

    Thanks!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Truthbetold View Post
    If f(2)= 3 and f'(2)= 5, find an equation (a) the tangent line, and (b) the normal line to the graph of y=f(x) at the point where x=2.

    Guess:
    f(2)=3 refers to the answer of a basic derivative ( lim as h--> 0 \frac {f(x-h) -f(x)}{h} )of an unknown equation with x=2.

    f'(2)=5 refers to the answer of the same equation in the other definition
    lim as x--> a \frac {f(x)-f(a)}{x-a} with x=2.

    Either that f(2) in some equation of the derivative = 3 and 5.
    I'm inclined to believe the latter.

    Thanks!
    you're thinking too hard. f(2) = 3 means the line passes through (2,3), f'(2) = 5 means the slope of the line is 5 at the point x = 2. just use the point slope form, no calculus needed (the normal line of course has slope -1/5, passing through the same point, again, use the point slope form for this)
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  3. #3
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    Oooooooooooooooooooooooooooooooooooooooooooh!
    Got it.

    Is there a difference in meaning for f(x) and f'(x)?
    My book gives the impression that they all mean, when it comes down to the nitty gritty, the same function.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Truthbetold View Post
    Oooooooooooooooooooooooooooooooooooooooooooh!
    Got it.

    Is there a difference in meaning for f(x) and f'(x)?
    My book gives the impression that they all mean, when it comes down to the nitty gritty, the same function.
    no. f(x) is a function, f'(x) is the derivative of the function f(x), the ' means first derivative. if you had f''(x) it would mean the second derivative of f(x), which means you take the derivative twice and so on
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