Question

Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = x + 16/x , [0.2, 16}

Answer 1

Find the stationary points.

f(x) = x + 16/x

f '(x) = 1 - 16/x ²

Solve f '(x) = 0.

1 - 16/x ² = 0   →   x ² = 16   →   (x - 4) (x + 4) = 0

→   x = -4, x = 4

Check the value of f at the stationary points. x = -4 is not in the provided domain so we can omit it.

f (4) = 8

Check the value of f at the boundary of the domain.

f (0.2) = 401/5 = 80.2

f (16) = 17

Then over [0.2, 16], we have max(f ) = 401/5 and min(f ) = 8.