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

Question

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

Hamnetmj · Accepted Answer

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)

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=?

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