Question

Let a>0 & b>0 be two positive numbers and consider the function f(x) = x^a+x^−b. Find the positive value of x where f(x) achieves its minimum value.

a. x=1

b. x=a/b

c. x=(b/a)^1/a+b

d. x=(ab)^a+b

e. x=(a+b)^ab

f. x=(b/a)^a+b

Answer 1

Given, where

Differentiate with respect to ,

For critical points,

To find minimum value, take second derivative of function and plug critical points

, has minimum value.

Hence, Option c is correct.