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Determine the equation of the line that is tangent to y=8^x at the point on the curve where x=1/2

  • calculus -

    first the easy part,
    when x = 1/2 y = 8^(1/2) = √8
    so our point is (1/2, √8)

    I will take ln of both sides
    ln y = ln 8^x
    lny = x(ln8)
    (dy/dx) / y = ln8
    dy/dx = ln8(8^x)
    so at (1/2, √8)
    dy/dx = (ln8)(√8)

    so you have m = ln8(√8) and the point (1/2, √8)
    find the equation of the line.

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