Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Quick calculus question

Another quick question.

The question I've just completed reads:

I completed the proof and then got a little bit stuck on the second half of the question. What I was minded to do was square root both sides in order to obtain an expression in terms of plain old V and then use the chain rule. This turned out to be a bit problematic and, in the end, I had to resort to what I thought was a bit of a cheat, but it was the only way I could get the right answer. Instead, I did:

Solved

for x:

Found that

And solved for V: V = 36.

Question: Is this legitimate? More to the point, is it generally legitimate, cause I've got things like implicit differentiation in the back of my mind and something feels wrong about differentiating V² but I couldn't think how else to do it!

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Quick calculus question

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Bassaricyon neblina

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Quick calculus question

Thanks Olinguito, that's the sort of thing I would have expected, but the exercise in question occurs in the book before implicit differentiation is introduced, which is why I was hesitant to go down that kind of road.

Perhaps the book was expecting you to cheat, or perhaps I've simply got lucky.

Either way, I appreciate it and I'm more or less happy!

Edit: Although, surely

Is not V but V²? So I should have

Last edited by Au101 (2015-02-18 07:56:32)

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: Quick calculus question

Yes, you're right, I forgot to take the square root for V.

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Bassaricyon neblina