Question

Find the maximum and minimum of the following functions:

f(x) = x² + 16/x²

Answer 1

f(x) = x² + 16/x² 

∴ the roots of f'(x) = 0 are x₁ = 2 and x₂ = -2.

∴ by the second derivative test, f has minimum at x = 2 and minimum value of f at x = 2

∴ by the second derivative test, f has minimum at x = -2 and minimum value of f at x = -2

Hence, the function f has minimum value 8 at x = ± 2.