Question

Number 12 I’m not sure what to do

Answer 1

The curve in question is f(x) = e^x / x.  To find the slope of the tangent line to this curve, we differentiate, using the quotient rule:

           xe^x - e^x       e^x(x-1)

f '(x) = ----------------- = --------------  

              x^2                  x^2

at x=a=1, this slope is f '(1) = 0.

Find the value of the function at x = a =1:      f(1) = e

Thus, the tangent line has slope 0 and passes thru (1,e).  From this info we can readily surmise that the tangent line is horiz. and is given by y = e.