(adsbygoogle = window.adsbygoogle || []).push({}); Derivative with "constant" variables

Hi, I need some help figuring out this one situation that's got me thrown for a loop... not the first time, since my grasp of calculus is slippery at best.

1. The problem statement, all variables and given/known data

a and b are both positive constants

Drag(D) = av^2+b/v^2

I'm trying to find the value of V that would represent a min for D

2. Relevant equations

D=av^2+b/v^2

[tex]\frac{dD}{dv} = 2av-\frac{2b}{v^{3}}[/tex]

[tex]\frac{d^{2}D}{dv^{2}}= 2a+\frac{6b}{v^{4}}[/tex]

3. The attempt at a solution

If I learned this proper, the derivative = 0 at Max / Min points... so;

[tex]0=2av-\frac{2b}{v^{3}}[/tex]

[tex]\frac{2b}{v^{3}}= 2a[/tex]

[tex]v=\left(\frac{b}{a}\right)^{-1/4}[/tex]

I figured that with the second derivative that since all positive values of v will have a positive value of d^2D/dv^2, and so any point of the derivative =0 will be a minimum point for D.

Now, since this is homework, I don't necessarily need the correct answer, but if I could be pointed to where I'm gong wrong (if I am)... I don't know why, but having these variables as constants is really throwing me for a loop, and any help / advice here would be appreciated.

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# Homework Help: Derivative with constant variables

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