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Math Help - Equation of the tangent line at that point

  1. #1
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    Equation of the tangent line at that point

    Can someone please explain to me how to do this. It seems like a very straight forward question.

    Find the slope of the tangent line to the graph of each function at the given point. Write the equation of the tangent line at that point.

    f (x) = 2x-1 at (-3, -7)


    Now in the previous examples when there is division involved (-2/x at 1,-2) we use the formula f (x+h) - f(x) / h to solve the problem...


    I know for this problem we can take the derivative of 2x-1 which is 2, giving us the slope.

    but can we still use the formula as well? Just in case i'm not sure if the formula is necessary or not. but how would you solve this?
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    Quote Originally Posted by agent2421 View Post
    Can someone please explain to me how to do this. It seems like a very straight forward question.

    Find the slope of the tangent line to the graph of each function at the given point. Write the equation of the tangent line at that point.

    f (x) = 2x-1 at (-3, -7)


    Now in the previous examples when there is division involved (-2/x at 1,-2) we use the formula f (x+h) - f(x) / h to solve the problem...


    I know for this problem we can take the derivative of 2x-1 which is 2, giving us the slope.

    but can we still use the formula as well? Just in case i'm not sure if the formula is necessary or not. but how would you solve this?
    Dear agent2421,

    Yes. The formula you are telling about is in fact the definition of the derivative; If you have a function f the derivative, f'(x) is defined as,

    f'(x)=\displaystyle\lim_{h\rightarrow{0}}\frac{f (x+h)-f(x)}{h}

    In this case, f(x)=2x-1

    Therefore f'(x)=\displaystyle\lim_{h\rightarrow{0}}\frac{[2(x+h)-1]-(2x-1)}{h}=\displaystyle\lim_{h\rightarrow{0}}\frac{2h  }{h}=2

    Hope you understood.
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  3. #3
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    Thanks. What are the -3 and -7 used for then? And what would the be equation of the tangent line at that point?
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    Quote Originally Posted by agent2421 View Post
    Thanks. What are the -3 and -7 used for then? And what would the be equation of the tangent line at that point?
    Sketch the graph of y = f(x) = 2x - 1. Now answer your own questions.
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    Quote Originally Posted by agent2421 View Post
    Thanks. What are the -3 and -7 used for then? And what would the be equation of the tangent line at that point?
    Do you not recognize that y= 2x- 1 is a line?
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