How do you show that a function has no local minimum Screen

Question

How do you show that a function has no local minimum

C(x) = 150 +12; — 0.01952 + 0.02953, 0 lt; a: where a: is measured in units of hundreds.
(a) Show that C(m) has no local minimum. (b) What level of production minimizes the average cost per unit?

(2) The weekly cost (in dollars) of producing as units of a certain commodity is given by
C(x) = 150 +12; — 0.01952 + 0.02953, 0 lt; a: where a: is measured in units of hundreds.
(a) Show that C(m) has no local minimum. (b) What level of production minimizes the average cost per unit?
Math