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Math Help - Derivative help Calc 1

  1. #1
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    Derivative help Calc 1

    I have a homework assignment due tonight, and I feel like this guy ---->

    Here are the two questions I still do not understand

    1.) Write in slope intercept form the equation for the tangent line for the curve y=sin(x) at x=(pi/3).

    What I do know is the f'(x)=cos(x).
    Next, do I plug pi/3 into the derivative?? I'm lost at this point.

    2.) Use the definition of the derivative to compute the derivative of f(x) = squareroot(x-3)

    so.. f(x)=(x-3)^(1/2)
    could I do f(x)=(1/2)(x-3)^(-1/2) ?
    and where would I go after that?
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  2. #2
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    Quote Originally Posted by bassman111 View Post
    I have a homework assignment due tonight, and I feel like this guy ---->

    Here are the two questions I still do not understand

    1.) Write in slope intercept form the equation for the tangent line for the curve y=sin(x) at x=(pi/3).

    What I do know is the f'(x)=cos(x).
    Next, do I plug pi/3 into the derivative?? I'm lost at this point.

    the slope at x = pi/3 is f'(pi/3)



    2.) Use the definition of the derivative to compute the derivative of f(x) = squareroot(x-3)

    \textcolor{red}{f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}}

    \textcolor{red}{f(x) = \sqrt{x-3}}

    \textcolor{red}{f(x+h) = \sqrt{x+h-3}}
    ...
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  3. #3
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    Thank you, your response was helpful.

    As a quick follow up, if f(x)=cos(3x) does f'(x)=-3sin(3x)?
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  4. #4
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    Quote Originally Posted by bassman111 View Post
    Thank you, your response was helpful.

    As a quick follow up, if f(x)=cos(3x) does f'(x)=-3sin(3x)?
    that would be correct.
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  5. #5
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    Thank you for the help
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  6. #6
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    ok so if the derivative of the function is cos(x) and you plug in pi/3 in for x, and you check the unit circle you see that it is 1/2. So the slope then would be 1/2.

    Then when you put in pi/3 in the original equation you can get the (sqrt3)/2 as the y coordinate. Then y1-y2 = slope(x1-x2).

    y - (sqrt3)/2 = 1/2(x-pi/3)

    y= 1/2(x)- (pi/6) + (3(sqrt3)/6)

    then you have a standard y= mx+b by just doing the calculations. The only way to clean it up is to plug keep the decimal answer. So it would be:

    1/2x + 0.34342663

    But my answers aren't matching up with the previous advice, so maybe I'm missing something. I also need to apologize for not writing in cool math pictures. Hope this works, it will take me time to learn how to do that.
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  7. #7
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    As for your other problem with the definition of derivative, I'm getting

     \frac{1}{2\sqrt(x-3)}
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