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 2 years 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
 2 years 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

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

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1Well, 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.

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1All right, then that should be the case.

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0so you are telling me my answer is right?

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1Nope, 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.

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0how did you get 7h out from under the root?

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1How 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.

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1This is only useful for evaluating the limit.

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0I have no idea what you mean by that

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0why would I multiply the numerator and denominator by that?

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

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1If 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.

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0f(3+h) = \[\sqrt{7(3+h)}\]

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1My 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).

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0The original problem looks like the square root goes over the "t"

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

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

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1Where is there not a square root sign?

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0the 7h that is in the numerator of your third comment

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

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0oh that is weird it doesn't look like that in my browser

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0so my first comment is correct then

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0Square root of (7h) divided by h

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1No, it is not, as they are not equivalent statements.

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

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

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

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1Nope. I don't think there is any need to, unless you're taking limits.

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0so last thing square root of x*y is equal to square root of x times the square root of y?

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0Never mind I just proved it.

znimon
 2 years ago
Best ResponseYou've already chosen the best response.0Thanks again I'll have to look up a khan academy video on that

LolWolf
 2 years ago
Best ResponseYou've already chosen the best response.1Yes, 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.
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