znimon Group Title 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

1. znimon Group Title

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

2. LolWolf Group Title

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.

3. znimon Group Title

This is pre-calc

4. LolWolf Group Title

All right, then that should be the case.

5. znimon Group Title

so you are telling me my answer is right?

6. znimon Group Title

/correct

7. LolWolf Group Title

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.

8. znimon Group Title

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

9. LolWolf Group Title

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.

10. LolWolf Group Title

This is only useful for evaluating the limit.

11. znimon Group Title

I have no idea what you mean by that

12. znimon Group Title

why would I multiply the numerator and denominator by that?

13. znimon Group Title

@LolWolf

14. znimon Group Title

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

15. znimon Group Title

Y sub 2*

16. LolWolf Group Title

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.

17. znimon Group Title

yours simplifies to -7

18. znimon Group Title

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

19. LolWolf Group Title

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).

20. znimon Group Title

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

21. LolWolf Group Title

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

22. znimon Group Title

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

23. znimon Group Title

@LolWolf

24. LolWolf Group Title

Where is there not a square root sign?

25. znimon Group Title

Over the "7h"

26. znimon Group Title

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

27. LolWolf Group Title

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

28. znimon Group Title

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

29. znimon Group Title

so my first comment is correct then

30. znimon Group Title

Square root of (-7h) divided by h

31. LolWolf Group Title

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

32. znimon Group Title

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

33. LolWolf Group Title

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

34. znimon Group Title

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

35. LolWolf Group Title

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

36. znimon Group Title

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

37. znimon Group Title

Never mind I just proved it.

38. znimon Group Title

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

39. LolWolf Group Title

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.