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gabycc12
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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
 2 years ago
 2 years ago
gabycc12 Group Title
find the critical numbers and the open intervals on which the function is increasing or decreasing. y=3x^3+12x^2+15x
 2 years ago
 2 years ago

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myininaya Group TitleBest ResponseYou've already chosen the best response.2
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
 2 years ago

ParthKohli Group TitleBest ResponseYou've already chosen the best response.0
lol. It took me time to realize that "critical numbers" just means "critical points". :P
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Do you know how to find y'?
 2 years ago

gabycc12 Group TitleBest ResponseYou've already chosen the best response.0
f'(x)= 9x^2+24x+5 correct??
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
(15x)'=15
 2 years ago

gabycc12 Group TitleBest ResponseYou've already chosen the best response.0
oh okay now what do i do after this ? f'(x)= 9x^2+24x+15
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Please refer to my instructions. Set f'(x)=0 and solve for x :)
 2 years ago

gabycc12 Group TitleBest ResponseYou've already chosen the best response.0
i cant seem to be able to solve for x i got 3x(3x+8)=15
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
This is a quadratic equation You may use the quadratic formula
 2 years ago

gabycc12 Group TitleBest ResponseYou've already chosen the best response.0
yeah i did that and i got 8 and 8 ; but the answers in the book are 1 and 5/3
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
So you have 9x^2+24x+15=0 correct?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
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
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
\[ax^2+bx+c=0 => x=\frac{b \pm \sqrt{b^24ac}}{2a}\] Did you use this formula?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Then you need to try again, because 8 and 8 is not what you should get.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
What is a=? What is b=? What is c=?
 2 years ago

gabycc12 Group TitleBest ResponseYou've already chosen the best response.0
a=9 b=24 c=15 correct??
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Sure are you could have used the equation I provided you So let's plug these numbers in that you have
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
\[x=\frac{24 \pm \sqrt{24^24(9)(15)}}{2(9)}\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.2
Use order of operations to evaluate what is inside the radical
 2 years ago

gabycc12 Group TitleBest ResponseYou've already chosen the best response.0
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!
 2 years ago
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