The average cost function associated with producing and marketing x un

1.	The average cost function associated with producing and marketing x units of an item is given by AC = 2x – 11 + \(\frac{50}{x}\). Find the range of values of the output x, for which AC is increasing.
Answer» AC increases when \(\frac{d}{dx}\)(AC) > 0 C = 2x – 11 + \(\frac{50}{x}\) \(\frac{dC}{dx}\) = 2 – 0 + 50(\(\frac{-1}{x^2}\)) = 2 – \(\frac{50}{x^2}\) \(\frac{d}{dx}\)(AC) > 0 2 – \(\frac{50}{x^2}\) > 0 2 > \(\frac{50}{x^2}\) 2x² > 50 x²> 25 x > 5

The average cost function associated with producing and marketing x units of an item is given by AC = 2x – 11 + \(\frac{50}{x}\). Find the range of values of the output x, for which AC is increasing.

Answer»

AC increases when \(\frac{d}{dx}\)(AC) > 0

C = 2x – 11 + \(\frac{50}{x}\)

\(\frac{dC}{dx}\) = 2 – 0 + 50(\(\frac{-1}{x^2}\)) = 2 – \(\frac{50}{x^2}\)

\(\frac{d}{dx}\)(AC) > 0

2 – \(\frac{50}{x^2}\) > 0

2 > \(\frac{50}{x^2}\)

2x² > 50

x²> 25

x > 5