Question

Local behavior questions! picture attachment below!

Answer 1

@jim_thompson5910 hey! you helped with my other questions, any chance you know about this stuff too?

Answer 2

f(x) = x^3 - 6x^2

what is f ' (x) ?

Answer 3

hmm im not sure..you dont plug in 0 do you?

Answer 4

have you learned about derivatives?

Answer 5

that word doesnt sound familiar but i think we have!! hah

Answer 6

is this calculus class?

Answer 7

no it is classified as advanced algebra but it sure seems like calculus material. i just did the problem, would the answer be D?

Answer 8

this is definitely an unfair problem if you haven't learned about calculus and derivatives

Answer 9

yes ive never taken any calculus class. this material is all new.

Answer 10

but we can at least use the graph

Answer 11

yes thats what i did!

Answer 12

notice how the graph continues on forever as you go down the left side

so there is NO global min

Answer 13

at the same time, the graph continues on forever as you go up the right side

so there is NO global max

Answer 14

there are no global extrema

Answer 15

however, there is a peak at x = 0 so this is where the local max is

there is a valley at x = 4 which is where the local min is

Answer 16

there are no global extrema but there are 2 local extrema (1 local max and 1 local min)

Answer 17

ahh so it would be B. i have a hard time telling the difference between global and local max/min.

Answer 18

global refers to the entire domain unless otherwise explicitly stated

Answer 19

local is just within a very specific interval (usually a small interval)

Answer 20

yes B

Answer 21

thank you! i have some others, would you be able to check my answers? if you dont have time thats fine!

Answer 22

sure I can do that

Answer 23

awsome! thank you. here is another. im not positive on my answer.

Answer 24

its just telling you to find the polynomial function that goes with the graph. i know the leading coefficient cant be a negative number so that left me to A and B.

Answer 25

actually im positive it must be A! i just checked again.

Answer 26

lol forget about that. i dont know why im so stupid. okay i will send you the next one that im actually unsure about!

Answer 27

choice A is correct

Answer 28

you aren't stupid

Answer 29

haha i may not be stupid but i was just acting stupid! i should have known. thank you though. here is one i am unsure about. you have to factor first right?

Answer 30

im bad with these types of questions where you have to factor.

Answer 31

yes factor as much as you can

Answer 32

tell me what you get

Answer 33

hmm 2x^2(6+x) (-6+x)?

Answer 34

very good

Answer 35

you can also write it as 2x^2(x+6)(x-6)

Answer 36

2x^2(x+6)(x-6) = 0

2x^2 = 0 or x+6 = 0 or x-6 = 0

solve each equation for x

Answer 37

Okay, so now the answer i get would be B! it has to be because 2x^2=0 is going to be 0 and it is going to be touch. and there are still the other two equations so it has to be B right?

Answer 38

correct

Answer 39

even multiplicity ----> touch
odd multiplicity ----> cross

Answer 40

perfect thanks! and this is the last one. im pretty sure im right, just want to make sure though.

Answer 41

did you graph this function?

Answer 42

i did. it only has one turning point

Answer 43

yes, notice how it peaks out at (12.5, 156.25)

this is the highest the graph goes...for the ENTIRE domain. So this is both a local max and a global max

Answer 44

there is no local min or no global min because it continues on forever downward

Answer 45

ohhh okay. so the answer would be D.

Answer 46

good

Answer 47

thank you!! you explained it really well. that was the last question i was unsure about! thank you again!

Answer 48

no problem