find the critical numbers and the open intervals on which the function is increasing or decreasing. y=3x^3+12x^2+15x

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find the critical numbers and the open intervals on which the function is increasing or decreasing. y=3x^3+12x^2+15x

Mathematics
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To find critical numbers for a polynomial you need to find f'(x) And set f'(x)=0 And solve for x These solutions to f'(x) will be your critical numbers
lol. It took me time to realize that "critical numbers" just means "critical points". :P
Do you know how to find y'?

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f'(x)= 9x^2+24x+5 correct??
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(15x)'=15
oh okay now what do i do after this ? f'(x)= 9x^2+24x+15
Please refer to my instructions. Set f'(x)=0 and solve for x :)
i cant seem to be able to solve for x i got 3x(3x+8)=15
This is a quadratic equation You may use the quadratic formula
yeah i did that and i got 8 and -8 ; but the answers in the book are -1 and -5/3
So you have 9x^2+24x+15=0 correct?
You could divide both sides by 3 since each term has a common factor 3 Giving you 3x^2+8x+5=0 Now you can do the quadratic formula but this is also pretty easy to factor
\[ax^2+bx+c=0 => x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\] Did you use this formula?
yes i did
Then you need to try again, because 8 and -8 is not what you should get.
What is a=? What is b=? What is c=?
a=9 b=24 c=15 correct??
Sure are you could have used the equation I provided you So let's plug these numbers in that you have
\[x=\frac{-24 \pm \sqrt{24^2-4(9)(15)}}{2(9)}\]
Use order of operations to evaluate what is inside the radical
ohhh okay i see what i did wrong i multiplied -24 by 6 instead of adding and subtracting. Thank you so much for your help!

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