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    Equations of Tangent Lines

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    What is the equation of the tangent line to f(x) = bar e^(x^2) at x = 2?

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    Answer: D

    Since f(x)=e^(x^2), then f'(x)=2xe^(x^2)
    At the point x=2, we have
    f(2)=e^4 and f'(2)=4e^4
    Then the tangent line is
    y-f(2)=f'(2)(x-2), then
    y-e^4=4e^4(x-2)=4e^4 x - 8e^4
    Then we get
    y=4e^4 x - 7e^4.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 6:57 pm ad1c9bdddf>
    https://brainmass.com/math/calculus-and-analysis/equations-tangent-lines-152123

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