Use the first and second derivative of f(x)=e^(1/x), together with asymptotes to sketch the graph.?

The first derivative tells us whether the function is increasing or decreasing on specific period.

f'(x) = (-1/x^2) * e^(1/x)

Set this equal to 0. Then make intervals where it crosses zero. Find out where it is increasing and decreasing and you'll be able to solve for local max/min.

The second derivative tell us us about the curvature of the function. This well tell you where it is concave or convex and you will be able to find possible inflection points. Combined with asymptotes, you can graph this function with pretty great accuracy.

you're able to have the equation a million. discover THE area discover the barriers of y . . if y will boost infinitely then it has no shrink 2. discover THE INTERCEPTS replace y=0 and remedy for x . . . it fairly is the x-intercept replace x=0 and remedy for x . . . it fairly is the y-intercept 3. discover THE HORIZONTAL AND VERTICAL ASSYMPTOTES equate the denominator to 0 . . . the value of the variable is the assymptote 4. discover THE periods OF boost OR shrink remedy for the derivative. . . . 5. discover THE interior of reach MAX and native MIN VALUES, IF ANY remedy for the derivative and equate to 0. . . then remedy the different variable