The minimum value of (x^2 +250/x ) is : A. 75 B. 50 C. 25 D. 55 ​

Question

The minimum value of (x² + \(\frac{250}{x}\)) is :

A. 75 

B. 50 

C. 25 

D. 55

Answer 1

Option : (A)

f(x) = x² + \(\frac{250}{x}\)

Differentiating f(x) with respect to x, we get

 f'(x) = 2x - \(\frac{250}{x^2}\)

Differentiating f’(x) with respect to x, we get

 f''(x) = 2 + \(\frac{500}{x^3}\)

For minima at x = c, 

f’(c) = 0 and f’’(c)>0 f’(x) = 0 

⇒ x³ = 125 or x = 5 

f’’(5) = 7>0 

Hence, 

x = 5 is a point of minima for f(x) and f(5) = 75 is the minimum value of (x).