Data Structures, Algorithms, & Applications in C++
Chapter 18, Exercise 13

We can establish this by showing that the derivative is a nondecreasing function of x for the given values of a, b, and x.

When b = 0, the derivative of the given function is ax^a-1, which is a nondecreasing function when a >= 1 and x >= 1.

When b > 0 and an integer, the derivative of the given function is


ax^a-1 log^bx + bx^a-1 log^b-1x


= x^a-1 log^b-1x (a log x + b)

This is a nondecreasing function also.

Data Structures, Algorithms, & Applications in C++ Chapter 18, Exercise 13

Data Structures, Algorithms, & Applications in C++
Chapter 18, Exercise 13