Question

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

Answer 1

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

Answer 2

lol. It took me time to realize that "critical numbers" just means "critical points". :P

Answer 3

Do you know how to find y'?

Answer 4

f'(x)= 9x^2+24x+5
correct??

Answer 5

close

Answer 6

(15x)'=15

Answer 7

oh okay now what do i do after this ?
f'(x)= 9x^2+24x+15

Answer 8

Please refer to my instructions.
Set f'(x)=0 and solve for x :)

Answer 9

i cant seem to be able to solve for x
i got
3x(3x+8)=15

Answer 10

This is a quadratic equation
You may use the quadratic formula

Answer 11

yeah i did that and i got 8 and -8 ; but the answers in the book are -1 and -5/3

Answer 12

So you have 9x^2+24x+15=0
correct?

Answer 13

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

Answer 14

\[ax^2+bx+c=0 => x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\]
Did you use this formula?

Answer 15

yes i did

Answer 16

Then you need to try again, because 8 and -8 is not what you should get.

Answer 17

What is a=?
What is b=?
What is c=?

Answer 18

a=9 b=24 c=15
correct??

Answer 19

Sure are you could have used the equation I provided you
So let's plug these numbers in that you have

Answer 20

\[x=\frac{-24 \pm \sqrt{24^2-4(9)(15)}}{2(9)}\]

Answer 21

Use order of operations to evaluate what is inside the radical

Answer 22

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!