# Examine the Function F (X) = X + 25 X for Maxima and Minima - Mathematics and Statistics

Sum

Examine the function f(x) = x + 25/x  for maxima and minima

#### Solution

f(x) = x + 25/x

f'(x) = 1 - 25/x^2

f''(x) = 50/x^3

f has maxima or minima if

f'(x) = 0

1 - 25/x^2 = 0

x^2 - 25 = 0

∴ x = 5 , x = -5

f''(5) = 50/5^3

f''(5) = 2/5 > 0

f''(-5) = 50/(-5)^3

f''(-5) = (-2)/5 < 0

∴ From equation (ii) f has maxima at x = - 5. And maximum value of f is

f_(max) = f(-5)

= -5 + 25/-5

= -10

Also from equation (i) f has minima at x = 5
And minimum value of f is

f_(min) = f(5)

= 5 + 25/5

f_(min) = 10

Concept: Maxima and Minima
Is there an error in this question or solution?