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Math Help - Find the equation of the tangent line to the curve.

  1. #1
    Junior Member mant1s's Avatar
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    Find the equation of the tangent line to the curve.

    Hi guys,

    Could someone take a look at my work.. im lost.

    Problem:
    Code:
    Find the equation of the tangent line to the curve  
    y= 4 tan x  at the point ( pi/4 , 4). 
    
    The equation of this tangent line can be written in the form y = mx+b
    my work..

    Code:
    using y-y1 = m(x-x1)
    
    y - 4tan(x) = 4tan(x- (pi/4))
    y - 4tan(x) = 4tan(x) - (pi tan (x))
    y = 8tan(x) - pi tan(x)
    
    m = 8tan(x)
    b = pi tan (x)
    Where did I go wrong? How do I get the equation from the point and the tangent line?
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  2. #2
    Junior Member Rachel.F's Avatar
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    is it the answer?
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mant1s View Post
    Hi guys,

    Could someone take a look at my work.. im lost.

    Problem:
    Code:
    Find the equation of the tangent line to the curve  
    y= 4 tan x  at the point ( pi/4 , 4). 
    
    The equation of this tangent line can be written in the form y = mx+b
    my work..

    Code:
    using y-y1 = m(x-x1)
    
    y - 4tan(x) = 4tan(x- (pi/4))
    y - 4tan(x) = 4tan(x) - (pi tan (x))
    y = 8tan(x) - pi tan(x)
    
    m = 8tan(x)
    b = pi tan (x)
    Where did I go wrong? How do I get the equation from the point and the tangent line?
    The function is y=4\tan x. To find the slope for any x value, differentiate it. We now see that y^{\prime}=4\sec^2x. Since we're looking for the eqn of a tangent at \left(\tfrac{\pi}{4},4\right), we want to find the slope of the function at \frac{\pi}{4}. So it follows that y^{\prime}\!\left(\tfrac{\pi}{4}\right)=4\sec^2\le  ft(\tfrac{\pi}{4}\right)=4\left(\sqrt{2}\right)^2=  4\cdot2=8. This is your slope in your tangent line equation.

    So using the point-slope equation, we have y-4=8\left(x-\tfrac{\pi}{4}\right)\implies y=8x-2\pi+4

    Does this make sense?
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  4. #4
    Junior Member mant1s's Avatar
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    Rachel and Chris,

    You guys rock! It makes sense to me now. I wasn't differentiating and it was screwing me up royally. Thanks for your time!

    -M
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