What is the equation of the tangent line of f(x)=(2x+1)/(x+2) at x=1?

1 Answer
Nov 10, 2015

y-1=(1/3)(x-1)

Explanation:

You are given the x value so plug that into the original equation to find y: (2(1)+1)/((1)+2) and you get 1, now we have a point (1,1) so we now know we are looking for the slope of the tangent line at (1,1)

The tangent line is the derivative of the equation so find the derivative using the quotient rule:
(g(x)f'(x)-f(x)g'(x))/(g(x)^2) where g(x) is the denominator and f(x) is the numerator so you get:

f'(x)=3/(x+2)^2 as the derivative
Now plug in 1 for the x value and f'(x) will return you with the slope or m. You now get 1/3 for f'(x) this is you m value now place everything in equation form:

y-1 = 1/3(x-1)
solve for y if necessary