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)

Question

Please show steps.

Thanks.

Answer 1

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)

Answer 2

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