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.
Hi
First step:
You have to find the derivative
$\displaystyle y' = 2*2x + (-1)480/(x^2)$
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 $\displaystyle y(120^{1/3}) \approx 146$