Answer:
Step-by-step explanation:
Positive number of x = ?
Such that the sum of numbers 25x and 1/x is as small as possible.
Step 1:
Let's use differentiation to determine the minimum sum
Y = 25x + 1/xdy
Y = 25x + x^-1 dy
dy/dx = 25.x^(1-1) + x^(-1-1)
= 25.x^0 + x^(-2)
= 25(1) + x^-2
= 25 + 1/x^2
Step 2:
Let's find the value of x
Take dy/dX = 0
0 = 25 + 1/x^2
(Make x the subject of the formula)
25 = 1/x^2
1/25 = x^2
(find the square root)
1/5 = x
Step 3:
Substitute the value of x (that is our calculated 1/5) into the question so as to determine the sum of 25x and 1/x
Sum = 25x + 1/x
= 25.(1/5) + 1/(1/5)
= 5 + 5
= 10
Therefore,
When x = 1/5, the sum of 25x and 1/x is 10
That's the minimum value over the open interval x>0.
I hope this helps.
