Determining Intervals 1

[Michael13]

Thanks for the help!!

Determine the intervals on which the following function is increasing and decreasing and classify each of the critical points as a relative minimum, maximum, or neither.

f(x)=-8x^5+10x^4+160x^3-200

 

[Quaid]

Determine the intervals on which the following function is increasing and decreasing and classify each of the critical points as a relative minimum, maximum, or neither.

f(x)=-8x^5+10x^4+160x^3-200

Hi Michael:

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Is there something in the exercises statement that you don't understand?

What did you get for f'(x)?

Please explain where you are stuck.

Thank you.

 

[Michael13]

Sorry everyone.

Sorry all, I just wanted to throw them on here real quick. This is what I have so far:

I found the f'= -40x^4+40x^3+480x^2
then I brought it all = to 0
and factored it out to find -40x^2 (x-4)(x+3)
This gave me critical points of 0, 4, -3

I believe that the minimum is -3, the 0 is level, and the maximum is 4
I believe that the function is increasing on (-3, 0)(0, 4) and decreasing (-infinity, -3)(4, infinity)

am i right? thanks again

 

[srmichael]

Sorry all, I just wanted to throw them on here real quick. This is what I have so far:

I found the f'= -40x^4+40x^3+480x^2
then I brought it all = to 0
and factored it out to find -40x^2 (x-4)(x+3)
This gave me critical points of 0, 4, -3

I believe that the minimum is -3, the 0 is level, and the maximum is 4
I believe that the function is increasing on (-3, 0)(0, 4) and decreasing (-infinity, -3)(4, infinity)

am i right? thanks again

Looks good to me. Although I may say 0 is a possible Point of Inflection and not "level".