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Math Help - Find equation of tangent line

  1. #1
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    Find equation of tangent line

    If f(Pi/8) = 0 and f '(x) = 3/2 + (cos (2x))^2, find the equation of the tangent line to the graph of this function at the point (Pi/8, 0).
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  2. #2
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    Quote Originally Posted by zweevu View Post
    If f(Pi/8) = 0 and f '(x) = 3/2 + (cos (2x))^2, find the equation of the tangent line to the graph of this function at the point (Pi/8, 0).

    A tangent line has the following form for all functions

    y-y_0=m(x-x_0)

    Where (x_0,y_0) is the point at which you want the line to be tangent and m= the derivative evalauted at the point (x_0,y_0)

    So f'(\frac{\pi}{8})=\frac{3}{2}+\cos^2(2\cdot\frac{\  pi}{8})

    =\frac{3}{2}+\cos^2(\frac{\pi}{4})=\frac{3}{2}+\le  ft ( \frac{\sqrt{2}}{2}\right )^2

    =\frac{3}{2}+\frac{2}{4}=2

    I leave it to you to plug it into the formula I provided
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