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