Find the exact global maximum and minimum values of the func

Find the exact global maximum and minimum values of the function. If there is no global minimum or maximum enter \"NA\". f(x) = 5x - 5 ln x for x > 0 The global minimum is 1. The global maximum is NA.

Solution

f(x) = 5x - 5lnx

f\'(x) = 5 - 5/x

5 -5/x =0 ; x=1

Use 2nd derivative test to find maxima/minima:

f\"(x) = 5/x^2 ; f\"(1) = 5 >0 at the critical point

So, its a minima

Minima = ( 1, 5)

We have to find Minima values of f(x) = 5

Maxima = n.a