




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.