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

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myininayaBest 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
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.0
lol. It took me time to realize that "critical numbers" just means "critical points". :P
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Do you know how to find y'?
 one year ago

gabycc12Best ResponseYou've already chosen the best response.0
f'(x)= 9x^2+24x+5 correct??
 one year ago

gabycc12Best ResponseYou've already chosen the best response.0
oh okay now what do i do after this ? f'(x)= 9x^2+24x+15
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Please refer to my instructions. Set f'(x)=0 and solve for x :)
 one year ago

gabycc12Best ResponseYou've already chosen the best response.0
i cant seem to be able to solve for x i got 3x(3x+8)=15
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
This is a quadratic equation You may use the quadratic formula
 one year ago

gabycc12Best 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
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
So you have 9x^2+24x+15=0 correct?
 one year ago

myininayaBest 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
 one year ago

myininayaBest 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?
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Then you need to try again, because 8 and 8 is not what you should get.
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
What is a=? What is b=? What is c=?
 one year ago

gabycc12Best ResponseYou've already chosen the best response.0
a=9 b=24 c=15 correct??
 one year ago

myininayaBest 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
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
\[x=\frac{24 \pm \sqrt{24^24(9)(15)}}{2(9)}\]
 one year ago

myininayaBest ResponseYou've already chosen the best response.2
Use order of operations to evaluate what is inside the radical
 one year ago

gabycc12Best 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!
 one year ago
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