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Mathematics 22 Online
OpenStudy (anonymous):

Let f(x)=x^3−12x^2+45x+3. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima).

OpenStudy (rational):

show ur work

OpenStudy (anonymous):

I found that the zeros are 3 and 5 and when i plugged them into f(x) i got -97 and 39. That's all the work i have so far. I'm not sure what to do next.

OpenStudy (freckles):

you don't need to find the zeros of f you need to find the zeros of f' is that what you mean?

OpenStudy (freckles):

ok yes x=3 and x=5 are the zeros of f' good work there

OpenStudy (freckles):

So you need to see if f'>0 or <0 for each interval

OpenStudy (freckles):

so you need to test (-inf,3) (3,5) (5,inf)

OpenStudy (freckles):

by choosing a number from those intervals and pluggin them into f'

OpenStudy (freckles):

f'>0 means f is increasing f'<0 means f is decreasing

OpenStudy (anonymous):

ok so i got f is decreasing in the interval (3,5)

OpenStudy (anonymous):

and for when f is increasing i got (-inf, 3) U (5, inf) but the computer is marking it wrong for some reason. is this wrong?

OpenStudy (freckles):

hey you there?

OpenStudy (freckles):

what numbers did you plug into f'?

OpenStudy (freckles):

and what do you have for f'

OpenStudy (freckles):

\[f(x)=x^3−12x^2+45x+3 \\ f'(x)=3x^2-24x+45=3(x-8x+15)=3(x-5)(x-3) \\ \text{ sign of } f'(0) \text{ is positive } \text{ so increasing on } (-\infty,3) \\ \text{ sign of } f'(2) \text{ is negative so decreasing on } (3,5) \\ \text{ sign of } f'(6) \text{ is positive so increasing on } (5,\infty) \\ \text{ SUMMARY: } \\ \text{ increasing on } (-\infty,3) \cup (5,\infty) \\ \text{ decreasing on } (3,5)\] looks good to me

OpenStudy (freckles):

you can sorta draw this now if you want and get an idea of where your max and min occur

OpenStudy (freckles):

It looks like you attempted to find the max and min values by pluggin in x=3 and x=5 this information was not requested by your problem but I'm not getting either of those values you got

OpenStudy (anonymous):

this what i plugged into the computer

OpenStudy (freckles):

I see

OpenStudy (freckles):

did you read the note

OpenStudy (freckles):

it says to seperate your intervals with a comma you aren't wrong you just have a picky software

OpenStudy (freckles):

(-inf,3),(5,inf)

OpenStudy (anonymous):

ohh yes i see lol thank you!!

OpenStudy (freckles):

np :)

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