Question

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

Answer 1

I have \[\sqrt{-7h}/h\] but it says that is wrong and I can't figure out why

Answer 2

Well, the 'average' rate of change for some interval \([a,b]\) (non-calculus, please tell me if you need otherwise) would be:
\[
\Delta f_{avg}=\frac{f(b)-f(a)}{b-a}
\]Try using that.

Answer 3

This is pre-calc

Answer 4

All right, then that should be the case.

Answer 5

so you are telling me my answer is right?

Answer 6

/correct

Answer 7

Nope, sorry. Using the above, we find, for \(f(t)=\sqrt{-7t}\)
\[
\frac{f(-3+h)-f(-3)}{-3+h+3}=\frac{\sqrt{21-7h}-\sqrt{21}}{h}
\]If you need further simplification of the above, please tell me.

Answer 8

how did you get -7h out from under the root?

Answer 9

How does one? You can't, you'd have to multiply both the numerator and denominator by \(\sqrt{21-7h}+\sqrt{21}\), but then it would end up on the denominator.

Answer 10

This is only useful for evaluating the limit.

Answer 11

I have no idea what you mean by that

Answer 12

why would I multiply the numerator and denominator by that?

Answer 13

@LolWolf

Answer 14

My 7 sub 2 is \[\sqrt{21-7h}\]

Answer 15

Y sub 2*

Answer 16

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.

Answer 17

yours simplifies to -7

Answer 18

f(-3+h) = \[\sqrt{-7(3+h)}\]

Answer 19

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).

Answer 20

The original problem looks like the square root goes over the "t"

Answer 21

Yes, and that's how I computed it. What do you feel is wrong with my expression?

Answer 22

I don't understand how there is no square root sign over the 7h in your third comment

Answer 23

@LolWolf

Answer 24

Where is there not a square root sign?

Answer 25

Over the "7h"

Answer 26

the 7h that is in the numerator of your third comment

Answer 27

http://imgur.com/1fwvB
This is what I have in my browser and what has been typed.

Answer 28

oh that is weird it doesn't look like that in my browser

Answer 29

so my first comment is correct then

Answer 30

Square root of (-7h) divided by h

Answer 31

No, it is not, as they are not equivalent statements.

Answer 32

yeah it is because square root of (x+y) is equal to square root of x plus square root of y right?

Answer 33

No, it does not.
\[
\sqrt{a+b}\ne\sqrt{a}+\sqrt{b}
\]Unless a or b is zero.

Answer 34

oh jesus I feel like an idiot. So then your third comment does not simplify any further in pre calc?

Answer 35

Nope. I don't think there is any need to, unless you're taking limits.

Answer 36

so last thing square root of x*y is equal to square root of x times the square root of y?

Answer 37

Never mind I just proved it.

Answer 38

Thanks again I'll have to look up a khan academy video on that

Answer 39

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.