Question

F is a cubic polynomial written as f(x)=ax^3+bx^2+cx+d find conditions on a,b,c such as F has (i) two critical points. (ii) one critical point. (iii) no critical points. Using the results from above to solve: (b) If F has only one critical point, then x=?

Answer 1

So you know how to find critical numbers?

Answer 2

All I have is y prime. y=3ax^2+2b+c than use guad formula on that.

Answer 3

And when do you have 2 real solutions ?

Answer 4

When what is bigger than 0?

Answer 5

it starts with a d

Answer 6

discr....

Answer 7

and it is y=3ax^2+2bx+c

do you know what d word I'm talking about?

Answer 8

discrimination

Answer 9

discriminant

Answer 10

not discrimination
that is what happens when people don't like another group of people

Answer 11

Yea. My bad. sorry.

Answer 12

Im totally lost.

Answer 13

so recall
if you have y=ax^2+bx+c
two real solutions will happen if b^2-4ac>0
one real solution will happen if b^2-4ac=0
no real solutions will happen if b^2-4ac<0

Answer 14

So find the discriminant for your equation.

Answer 15

Yep. I have that. But i don't know how to find the discriminant for the equation.

Answer 16

\[y=Ax^2+Bx+C\]
\[D=B^2-4AC\]
Your equation is
\[y'=3ax^2+2bx+c\]

What is A for our equation?

Answer 17

have no idea

Answer 18

A is the thing in front of x^2
what is the thing in front of your x^2?

Answer 19

3

Answer 20

what about 3a
is not that in front of x^2?

Answer 21

Yea. 3a

Answer 22

I didn't think it was important to write the A

Answer 23

look we are comparing these equations:
\[y=Ax^2+Bx+C\]
\[y=3ax^2+2bx+c\]
A=3a <--these were both the things in front of x^2
now
what is B=?

Answer 24

2b

Answer 25

ok and course C=c

so what is our discriminant D?

Answer 26

d just goes away. i thnk

Answer 27

\[D=B^2-4AC\]
what is D with the values we just found for A,B, and C?

Answer 28

no clue

Answer 29

well you told B=2b and A=3a and C=c
so you can find D b replacing those values in D

Answer 30

is d=3

Answer 31

is that the answer?

Answer 32

No.