Find the slope and the equation of the line tangent to f(x)= (2x-1)/(x+1) at x= 2 A) The slope of the line tangent to f(x) at x=2 is what? B) The equation of the tangent line is y=?

hogwartsxhoe5t 2022-10-12 Answered
Find the slope and the equation of the line tangent to f ( x ) = 2 x 1 x + 1 at x= 2
A) The slope of the line tangent to f(x) at x=2 is what?
B) The equation of the tangent line is y=?
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Answers (1)

Hamnetmj
Answered 2022-10-13 Author has 21 answers
Given:
f ( x ) = 2 x 1 x + 1 f ( x ) = d d x ( 2 x 1 x + 1 ) = ( x + 1 ) d d x ( 2 x 1 ) ( 2 x 1 ) d d x ( x + 1 ) ( x + 1 ) 2 = 2 ( x + 1 ) ( 2 x 1 ) ( x + 1 ) 2 = 3 ( x + 1 ) 2
Slope of the tangent at x=2 is
m = f ( 2 ) = 3 ( 2 + 1 ) 2 = 3 ( 3 ) 2 = 1 3 (Answer)
Now, f ( 2 ) = 2 2 1 2 + 1 = 4 1 3 = 3 3 = 1
Equation of tangent at x=2 is given by
y f ( 2 ) = m ( x 2 ) ; m =  slope of the tangent  = 1 3
or,  y 1 = 1 3 ( x 2 ) or,  y = 1 3 ( x 2 ) + 1 (Answer)
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