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A function is given below. Determine the average rate of change of the function between x = 3 and x = 3 + h. f(t) = √7t
 one year ago
 one year ago
A function is given below. Determine the average rate of change of the function between x = 3 and x = 3 + h. f(t) = √7t
 one year ago
 one year ago

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znimonBest ResponseYou've already chosen the best response.0
I have \[\sqrt{7h}/h\] but it says that is wrong and I can't figure out why
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
Well, the 'average' rate of change for some interval \([a,b]\) (noncalculus, please tell me if you need otherwise) would be: \[ \Delta f_{avg}=\frac{f(b)f(a)}{ba} \]Try using that.
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
All right, then that should be the case.
 one year ago

znimonBest ResponseYou've already chosen the best response.0
so you are telling me my answer is right?
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
Nope, sorry. Using the above, we find, for \(f(t)=\sqrt{7t}\) \[ \frac{f(3+h)f(3)}{3+h+3}=\frac{\sqrt{217h}\sqrt{21}}{h} \]If you need further simplification of the above, please tell me.
 one year ago

znimonBest ResponseYou've already chosen the best response.0
how did you get 7h out from under the root?
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
How does one? You can't, you'd have to multiply both the numerator and denominator by \(\sqrt{217h}+\sqrt{21}\), but then it would end up on the denominator.
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
This is only useful for evaluating the limit.
 one year ago

znimonBest ResponseYou've already chosen the best response.0
I have no idea what you mean by that
 one year ago

znimonBest ResponseYou've already chosen the best response.0
why would I multiply the numerator and denominator by that?
 one year ago

znimonBest ResponseYou've already chosen the best response.0
My 7 sub 2 is \[\sqrt{217h}\]
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
If you wish to remove the \(h\) from the radical, you'd have to do that, but, of course, then the top expression ends up in the denominator. So, the point is that one cannot remove the \(h\) from such.
 one year ago

znimonBest ResponseYou've already chosen the best response.0
f(3+h) = \[\sqrt{7(3+h)}\]
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
My equation does not simplify. And, yes, that last statement is correct. Keep in mind: \[ \sqrt{a+b}\sqrt{a}=\sqrt{b}\\ \]Is *not* necessarily true (In fact, it is mainly true if b=0 or a=0).
 one year ago

znimonBest ResponseYou've already chosen the best response.0
The original problem looks like the square root goes over the "t"
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
Yes, and that's how I computed it. What do you feel is wrong with my expression?
 one year ago

znimonBest ResponseYou've already chosen the best response.0
I don't understand how there is no square root sign over the 7h in your third comment
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
Where is there not a square root sign?
 one year ago

znimonBest ResponseYou've already chosen the best response.0
the 7h that is in the numerator of your third comment
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
http://imgur.com/1fwvB This is what I have in my browser and what has been typed.
 one year ago

znimonBest ResponseYou've already chosen the best response.0
oh that is weird it doesn't look like that in my browser
 one year ago

znimonBest ResponseYou've already chosen the best response.0
so my first comment is correct then
 one year ago

znimonBest ResponseYou've already chosen the best response.0
Square root of (7h) divided by h
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
No, it is not, as they are not equivalent statements.
 one year ago

znimonBest ResponseYou've already chosen the best response.0
yeah it is because square root of (x+y) is equal to square root of x plus square root of y right?
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
No, it does not. \[ \sqrt{a+b}\ne\sqrt{a}+\sqrt{b} \]Unless a or b is zero.
 one year ago

znimonBest ResponseYou've already chosen the best response.0
oh jesus I feel like an idiot. So then your third comment does not simplify any further in pre calc?
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
Nope. I don't think there is any need to, unless you're taking limits.
 one year ago

znimonBest ResponseYou've already chosen the best response.0
so last thing square root of x*y is equal to square root of x times the square root of y?
 one year ago

znimonBest ResponseYou've already chosen the best response.0
Never mind I just proved it.
 one year ago

znimonBest ResponseYou've already chosen the best response.0
Thanks again I'll have to look up a khan academy video on that
 one year ago

LolWolfBest ResponseYou've already chosen the best response.1
Yes, that statement is true. Since: \[ a^2=n\\ b^2=m \]So we say: \[ nm=a^2b^2=(ab)^2 \]And all right, sure thing.
 one year ago
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