Plot the function

f(x) = xlnx

Step 1

The function f(x) = xlnx is defined for x strictly positive.

Sign and zeroes of f(x):

f(x) = 0 for lnx = 0 ie x = 1

f(x) < 0 for x <1

f(x) > 0 for x > 1

Calculation of f ' and f "

Step 3

Step 4

f"(x) =  > 0 when x > 0

f is concave up for x > 0

There is no inflection point since f "(x) = 0 has no solution.