Question

What are the coordinates of the turning point for the function f(x) = (x - 2)3 + 1?

Answer 1

take the derivative and equal to 0?

Answer 2

how do you take the derivative

Answer 3

what math problem is that i mean what class? calculus or algebra?

Answer 4

algebra

Answer 5

thats a line

Answer 6

is it (x-2)^3 or you typed it right

Answer 7

(-2, -1)

(-2, 1)

(2, -1)

(2, 1)
these are the answer choices

Answer 8

and yes

Answer 9

(2,1)

Answer 10

if you graph it thats the only point thats on line

Answer 11

oh okay

Answer 12

for that function when x = -2 then y should equal -11 so first choices are wrong

Answer 13

What are the possible numbers of positive, negative, and complex zeros of f(x) = -3x4 + 5x3 - x2 + 8x + 4?

do you know how to do this one?

Answer 14

I dont even know where to start

Answer 15

Use Descartes' Rule of Sign Changes

Answer 16

I dont know what that is

Answer 17

ive heard of it but dont really remember

Answer 18

You just count the amount of times the sign changes from positive to negative, this'll give you the amount of positive zeroes, then you change each sign to its opposite and count again and it'll give you the amount of negative zeroes. It's a bit more complicated than that but it gives you gist of it

Answer 19

i think 3 positive and 2 negative?

Answer 20

Positive: 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0

Positive: 1; negative: 3 or 1; complex: 2 or 0

Positive: 3 or 1; negative: 1; complex: 2 or 0

Positive: 4 or 2 or 0; negative: 2 or 0; complex: 4 or 2 or 0

these ar ethe answer choices

Answer 21

3 sign changes when in its original form mean there can be 3 or 1 positive zeroes
3 sign changes when the signs are changed mean there can be 3 or 1 negative zeroes
Due to the degree of the function we know it has to have 4 zeroes

Answer 22

So it seems like it's 3 or 1 positive, 1 negative and 2 or 0 complex

Answer 23

i am not sure i never learned any of that in algebra or matter of fact i have never had problems like that till university calculus 2 ( i am taking cal 2 right now)

Answer 24

That's what i figure atleast

Answer 25

yeah we got same positive i would go with 3 or 1 option haha

Answer 26

That's the right answer, it's Descartes' Rule, I also had this question before

Answer 27

positive 3 or 1?

Answer 28

okay ill look up descartes rule and see what thats all about lol

Answer 29

It's the third option: 3 or 1 positive, 1 negative, 2 or 0 complex

Answer 30

thank you guys!

Answer 31

no problem haha