Find the positive number such that the sum of 8 times this number and 7 times its reciprocal is as small as possible.

√56/8

Step-by-step explanation:

Let the number be x

f(x) = 8x + 7(1/x)

f(x) = 8x + 7/x

Differentiate f(x) with respect to x

f'(x) = 8x - 7/x = 0

8 - 7/x^2 = 0

(8x^2 - 7)/2 = 0

8x^2 - 7 = 0

8x^2 = 7

x^2 = 7/8

x = √7/8

x = √7 /√8

x = (√7/√8)(√8/√8)

x = (√7*√8) / √8*√8)

x = √56/8

answer: 7

step-by-step explanation: