znimon 3 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

1. znimon

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

2. LolWolf

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

This is pre-calc

4. LolWolf

All right, then that should be the case.

5. znimon

so you are telling me my answer is right?

6. znimon

/correct

7. LolWolf

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

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

9. LolWolf

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

This is only useful for evaluating the limit.

11. znimon

I have no idea what you mean by that

12. znimon

why would I multiply the numerator and denominator by that?

13. znimon

@LolWolf

14. znimon

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

15. znimon

Y sub 2*

16. LolWolf

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

yours simplifies to -7

18. znimon

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

19. LolWolf

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

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

21. LolWolf

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

22. znimon

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

23. znimon

@LolWolf

24. LolWolf

Where is there not a square root sign?

25. znimon

Over the "7h"

26. znimon

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

27. LolWolf

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

28. znimon

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

29. znimon

so my first comment is correct then

30. znimon

Square root of (-7h) divided by h

31. LolWolf

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

32. znimon

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

33. LolWolf

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

34. znimon

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

35. LolWolf

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

36. znimon

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

37. znimon

Never mind I just proved it.

38. znimon

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

39. LolWolf

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.