Question

For the polynomial function .............. find all local and global extrema.

Answer 1

\[f(x)=-2x^{2} -4x +16\]

Answer 2

@AdamK

Answer 3

A. No local extrema exist.
B. The only extrema point is (−1, 18).
C. The local and global extrema are: (0, -4), (0, 2) and (-1, 18).
D. No global extrema exist.

Answer 4

B. The only extrema point is (-1,18).

Answer 5

@SolomonZelman

Answer 6

@Michele_Laino

Answer 7

Hi!

Answer 8

Hi!

Answer 9

please you have to compute the first derivative of f(x)

Answer 10

Ok

Answer 11

How?

Answer 12

If you don't know calculus, do you know what kinda graph you have?
f(x)=ax^2+bx+c are well known to give what kinda graphs?

Answer 13

use this identity:
\[\left( {{x^n}} \right)' = n{x^{n - 1}}\]

Answer 14

you guys dont understand I have NO idea how to do this stuff

Answer 15

f(x)=ax^2+bx+c gives a graph of a parabola.
The a tells us if the vertex will be a min or a max.
If a>0, then the vertex will be a min.
If a<0, then the vertex will be a max.
Do you know how to find the vertex of a parabola ?

Answer 16

yes hold on one sec

Answer 17

ok so i did that then i replaced that for the x's and got the B one (-1,18)

Answer 18

Michele what do you think about this?

Answer 19

Sounds great.

Answer 20

I think that your answer is correct!

Answer 21

Awesome!

Answer 22

I actually got it right. I did some math and did what u said and got it HURRRRAHHHHHH

Answer 23

well thxs guys

Answer 24

who gets the medal?

Answer 25

thanks!

Answer 26

Just so you know @Michele_Laino was trying to show you a calculus way. I don't know if you know calculus or not but it is also cute.

Answer 27

I think that @freckles deserves a medal

Answer 28

I dont I'm only in Algebra 2

Answer 29

I don't care about medals. :p
Go to calculus. I promise it will be fun.

Answer 30

I will give @Michele_Laino a medal. :)

Answer 31

hey i got 19 more help freckles ok i give more medals

Answer 32

For the following graph, determine if the graph represents a polynomial function. If it is a polynomial function, then determine the number of turning points and the least degree possible

Answer 33

A. Yes, this graph represents a polynomial. There is one turning point and the least degree possible is two.
B. Yes, this graph represents a polynomial. There are two turning points and the least degree possible is two.
C. This is not a polynomial. There are no turning points.
D. This is not a polynomial. The entire graph is on one side of the vertical axis.

Answer 34

Do you know what a turning point is?

Answer 35

where the point on the graph rotates?

Answer 36

This is a point in where the graph changes direction.

Answer 37

like maybe it is going down and then it decides to go up
(or vice versa)
Where this happens, this is called a turning point

Answer 38

so then it wouild be A?

Answer 39

Sounds great

Answer 40

is that right?

Answer 41

are you just agreeing with me or am i right?

Answer 42

Yep.
It is a parabola. And parabola are polynomials.
Parabolas have deg 2 and 1 turning point .

Answer 43

dud AWESOMEEEEE

Answer 44

Use the Remainder Theorem to find the remainder resulting from the division:

Answer 45

\[(x ^{2}+5x-1) \div (x-1)\]

Answer 46

I'm going away from my computer now for a little bit after this next question so you might want to decide to post next one as a new question.

But for this one... Just find when the bottom is zero...That is solve x-1=0 for x
Then whatever you get for x there...plug into the x^2+5x-1 to find the remainder of (x^2+5x-1)/(x-1)

Answer 47

A. 5 B. -7 C. -5 D. 0

Answer 48

Have you performed first step? That is solve x-1=0 for x.
Then second step is: put that x into x^2+5x-1

Answer 49

yes

Answer 50

cool and what did you get?

Answer 51

I got -1

Answer 52

x-1=0 when x=?

Answer 53

-2

Answer 54

x-1=0
plus 1 on both sides

Answer 55

1 then

Answer 56

x-1=0
+1 +1
--- --
x+0=1
x=1
Yes the bottom is 0 when x is 1.
So now take that 1 in plug into the top polynomial

Answer 57

on both sides?

Answer 58

i got 5

Answer 59

wht do you mean both sides?

Answer 60

its A right

Answer 61

the top polynomial is x^2+5x-1
replace x with 1
and yes 5 is the remainder

this works because:
\[\frac{x^2+5x-1}{x-1}=Q(x)+\frac{R(x)}{x-1} \\ \text{ multiply } (x-1) \text{ on both sides } \\ x^2+5x-1=Q(x)(x-1)+R(x) \\ \text{pluggin \in x=1 will give us the remainder at x=1 } \\ 1^2+5(1)-1=Q(x)(1-1)+R(1) \\ 1+5-1=Q(x) \cdot 0 +R(1) \\ 5=R(1) \]

Answer 62

Awesome well since u gotta go ill fan u and if u ever get back on ill contact u @frackles