calculus

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Let f be a differentiable function such that f(3) = 2 and f'(3) = 5. If the tangent line to the graph of f at x = 3 is used to find an approximation to a zero of f, that approximation is?

So confused

  • calculus -

    y=mx+b f'(3)=5 means m=5
    y=5x+b but f(3)=2 means
    2=5*3+b, or b= -13

    tangent line y= 5x-13
    so the zero is 0=5x-13 x=13/5

  • calculus -

    That approximation is the intersection of
    the tangent and X-axis.
    The equation of the tangent:
    y-2=5(x-3)
    If y=0 then x=13/5

  • calculus -

    nice work, Mgraph.

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