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).
show ur work
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.
you don't need to find the zeros of f you need to find the zeros of f' is that what you mean?
ok yes x=3 and x=5 are the zeros of f' good work there
So you need to see if f'>0 or <0 for each interval
so you need to test (-inf,3) (3,5) (5,inf)
by choosing a number from those intervals and pluggin them into f'
f'>0 means f is increasing f'<0 means f is decreasing
ok so i got f is decreasing in the interval (3,5)
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?
hey you there?
what numbers did you plug into f'?
and what do you have for f'
\[f(x)=x^3−12x^2+45x+3 \\ f'(x)=3x^2-24x+45=3(x-8x+15)=3(x-5)(x-3) \\ \text{ sign of } f'(0) \text{ is positive } \text{ so increasing on } (-\infty,3) \\ \text{ sign of } f'(2) \text{ is negative so decreasing on } (3,5) \\ \text{ sign of } f'(6) \text{ is positive so increasing on } (5,\infty) \\ \text{ SUMMARY: } \\ \text{ increasing on } (-\infty,3) \cup (5,\infty) \\ \text{ decreasing on } (3,5)\] looks good to me
you can sorta draw this now if you want and get an idea of where your max and min occur
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
this what i plugged into the computer
I see
did you read the note
it says to seperate your intervals with a comma you aren't wrong you just have a picky software
(-inf,3),(5,inf)
ohh yes i see lol thank you!!
np :)
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