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Math Help - local linearization

  1. #1
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    Exclamation local linearization

    Let f(x)=3+cos(2x+(pi/2))

    Find the local linearization of the function at the point a=0.

    Use your linearization to find and approximation for f(0.4)
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  2. #2
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    Quote Originally Posted by thecount View Post
    Let f(x)=3+cos(2x+(pi/2))

    Find the local linearization of the function at the point a=0.

    Use your linearization to find and approximation for f(0.4)

    This is the same as finding the tangent line at the point x=0

    f'(x)=-2\sin\left( 2x+ \frac{\pi}{2}\right)

    f'(0)=-2\sin\left( \frac{\pi}{2}\right)=-2

    note that f(0)=3

    so the approximation is

    L(x)= -2x+3

    f(.4) \approx L(.4)=-2(.4)+3=2.2
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