Math Help - Minimum Point

1. Minimum Point

A problem I need help with.

y = 2x^2 + 480/x

I need to find the minimum point on that graph. Help would be greatly appreciated.

2. Hi

Originally Posted by Tesphen
A problem I need help with.

y = 2x^2 + 480/x

I need to find the minimum point on that graph. Help would be greatly appreciated.
First step:
You have to find the derivative

$y' = 2*2x + (-1)480/(x^2)$

second step:

Solve y' = 0

4x - 480/x² = 0

4x^3 - 480 = 0

4x^3 = 480

x^3 = 120

third step

find y'' and use x = 120^(1/3) to show y''(120^(1/3)) > 0 => minimum

hint: y'' = 960/x^3 + 4

last step

calculate y(120^(1/3)) = ... then you know the x-coordinate and y-coordinate of your minimum

I get $y(120^{1/3}) \approx 146$