## mathcalculus Group Title help help help!!!! Determine the extrema of f(x)= (-4)* x/ x^2+7 below on the given interval (a) on [1,4] The minimum is ?? and the maximum is ?? (b) on [1,5] The minimum is ?? and the maximum is ?? one year ago one year ago

1. mattt9 Group Title

is the x^2+7 all under the -4x

2. mathcalculus Group Title

yup

3. mathcalculus Group Title

yup$\frac{ (-4)*x}{ x^{2}+7}$

4. mathcalculus Group Title

@mattt9

5. mattt9 Group Title

and what was your derivative again?

6. mathcalculus Group Title

$\frac{ 1*(x ^{2}+ 7)-2x(-4)*x}{ (x^{2}+7) ^2 }$

7. mattt9 Group Title

are you sure that is correct wouldn't the derivative of the top be -4 not 1

8. mathcalculus Group Title

9. mathcalculus Group Title

maybe I did get it wrong. but i assumed since -4 is a constant i didn't use it...

10. mattt9 Group Title

|dw:1363315804166:dw|

11. mattt9 Group Title

you still use the constant if it's attached to the x like that.

12. mattt9 Group Title

(d/dx) of 2x is 2 right?

13. mathcalculus Group Title

oh so when you add you don't use the constant right?

14. mattt9 Group Title

as a random example

15. mattt9 Group Title

you wouldn't use the 7 when determining the derivative of the bottom since it is not attached to an x value.

16. mathcalculus Group Title

oh so you multiplied them which is -4x... then just fnd the derivative right>

17. mathcalculus Group Title

for example if it is -4+x then the derivative is 1.

18. mathcalculus Group Title

but if (-4)*x you keep them as -4 and find the derivative which is -4

19. mattt9 Group Title

right. then your derivative simplifies to : $\frac{ (4x^2-28) }{ (x^2+7)(x^2+7) }$

20. mathcalculus Group Title

awesome so let me do that.

21. mattt9 Group Title

okay

22. mathcalculus Group Title

how did you get 4x^2-28?

23. mathcalculus Group Title

what happened with the -6x?

24. mattt9 Group Title

what -6x

25. mathcalculus Group Title

i thought the derivative would be -4x^2-28-6x on the numerator

26. mattt9 Group Title

|dw:1363317471013:dw|

27. mattt9 Group Title

that's the numerator

28. mathcalculus Group Title

yeah but you wrote.. (4x2−28)/(x2+7)(x2+7)

29. mathcalculus Group Title

^**

30. mattt9 Group Title

yeah i know. but you had problems with the numerator. so i just showed you how i got the numerator

31. mattt9 Group Title

that is the full derivative.

32. mattt9 Group Title

anyways. you end up equation that to zero. $\frac{ (4x^2-28) }{ (x^2+7)(x^2+7) }=0$

33. mattt9 Group Title

the (x^2+7) cancels out and you are left with 4x^2-28 = 0

34. mattt9 Group Title

then solve for x to obtain a value for which the slope of the function is zero (a possible max or min)

35. mattt9 Group Title

at this point you will see that x = +-root(7) = +- 2.646

36. mattt9 Group Title

then you see that x = -2.626 is not in your given interval so you would not test this value. in the first interval of [1,4] you would test the x-values of x = 1 x = 4 and your found x value of x = 2.626 out of these three numbers one will be highest and one will be lowest, those should be your max and min for the function respectively. Let me know if any of that is incorrect.

37. mathcalculus Group Title

matt you make sense. are you there @mattt9

38. mathcalculus Group Title

so we don't test the critical points correct?

39. mattt9 Group Title

those are the critical points.

40. mathcalculus Group Title

a) because the intervals are [1,4] and b) intervals are from [1,5]

41. mattt9 Group Title

or at least 2.626 is for the function. 1 and 4 are for the interval. or maybe that terminology isn't used i can't remember but you would test all three of those points

42. mathcalculus Group Title

i did test them all out. i wrote (a) on [1,4] The minimum is -.695652 and the maximum is -1/2 (b) on [1,5] The minimum is -.625 and the maximum is -1/2 but when i click submit it says one of them is wrong...

43. mathcalculus Group Title

@mattt9 i would appreciate the help very much.

44. mattt9 Group Title

ummmmm what do you get when you plug in 2.626 into the fn.?

45. mathcalculus Group Title

2.626 into the fn.?

46. mathcalculus Group Title

47. mattt9 Group Title

(-4)(2.626)/(2.626^2+7) = -0.7559

48. mattt9 Group Title

that should be your minimum for both.

49. mathcalculus Group Title

youre right, i didn't see the negative by mistake.

50. mathcalculus Group Title

thank you!!

51. mattt9 Group Title

you areee welcome !