Question

Let f(x) = 4x(x² + 1)/(x² + (x² + 1)²), x ≥ 0 Then find the greatest and the least values of f(x). 

Answer 1

We have

Let g(x) = (x + 1/x)

⇒ g'(x) = (1 – 1/x²)

⇒  g'(x) = 0 gives (1 – 1/x²) = 0

⇒  x = ±1

Thus, the greatest value of f(x) is

= f(–1) = (4.(– 2))/( –2 + 1) = 8

and the least value of f(x) is

= f(1) = 4 . 2/(2 + 1) = 8/3