Find the minimum value of
Y=x^2+1/x
For x>0
Also,
If x,y, and z are positive integers such that x^2+y^2+z^2=174. What is the greatest value of x+y+z?
+128408 Find the minimum value of
Y=x^2+1/x
Take the derivative and set to 0
y ' = 2x - 1/x^2 = 0
So
2x - 1/x^2 = 0
2x = 1/x^2
2x^3 = 1
x^3 = 1/2
x = ∛(1/2) ⇒ this is the x value that minimizes the function
The minimum value is
[ (1/2)^(1/3) ] ^2 + 1 / (1/2)^(1/3) =
(1/2)^(2/3) + 1 / (1/2)^(1/3) ≈ 1.89
If x,y, and z are positive integers such that x^2+y^2+z^2=174. What is the greatest value of x+y+z?
The greatest value of x + y + z is when we have the triplet 5, 7, 10
And the sum = 22
