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Calc BC

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Let f be the function defined by f(x)=(4x-8)/(x^2+5x-14)

write an equation of the lien normal to the graph of f at x=1


how?

  • Calc BC -

    the line tangent to the graph at (x,y) has slope f'(x)

    f'(x) = -4/(x+7)^2
    f'(1) = -4/8^2 = -1/16

    The line normal to f thus has slope +16

    f(1) = 1/2

    So, now we have a point (1,1/2) and a slope: 16

    So, the line is

    y - 1/2 = 16(x-1)

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