Calculus

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For the function f(x) = x/(3x+1) find the equation of the line which is tangent to the curve f(x) at x=2. Solve analytically (an exact answer is required)


Please show steps.

Thanks.

  • Calculus -

    y–y0=f'(x0)*(x–x0)

    f'=1/(3x+1)^2

    x0=2

    y0=2/(3*2+1)=2/(6+1)=2/7

    f'(x0)=1/(3*2+1)^2=1/(6+1)^2=1/7^2=1/49


    y–y0=f'(x0)*(x–x0)

    y - 2/7 = 1/49*(x-2)

    y=(1/49)*x - 2/49 + 2/7

    y=(1/49)*x - 2/49 + 14/49

    y=(1/49)*x - 12/49

    y=(1/49)*(x-12)

  • Calculus -

    If You don't know how find derivation of x/(3x+1) in google type: calc101

    When you open page calc101com click option derivatives.In rectangle type:
    x/(3x+1)
    and click option DO IT

    You will see solution step by step

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