Question

How many local maxima and minima does the polynomial y=x^4-9x^2+7 have? Please show work.

Answer 1

find the derivaitve of this function, it will be 4x^3-18x
Then set it to zero: 4x^3-18x=0

Answer 2

you will get three extrema

Answer 3

2 min
and
1 max

Answer 4

what is the derivative?

Answer 5

4x^3-18x

Answer 6

I mean how do you find it?

Answer 7

if you are asking how to find min and max, you should know that we use the power rule to find the derivative of a polynomial

Answer 8

What is the power rule?

Answer 9

why are you asking about min or max if you dont know about the power rule? What grade are you in?

Answer 10

I'm going to be a high school junior and taking college algebra. It's just that I've never heard those terms before.

Answer 11

oh, okay i understand, i just though you were taking calculus or something, since we were dealing with min and max sorry

Answer 12

Its ok :) i get that a lot

Answer 13

not, that i think you are smart or anything, its just those words max and min signify calc for me

Answer 14

yeah we don't use those terms in class, and I haven't taken calc yet so I don't know what they mean

Answer 15

I'm not implying that I think I am a genius lol I know I am not

Answer 16

Minimums and maximums are where the function reaches it's highest and lowest points

Answer 17

I would use a graphing calculator to determine them, using the calculate button then max and min as appropriate. It will have no more than 4.

Answer 18

A function can only have as many minimums and maximums together as it's degree (the highest exponential form of 'x')

Answer 19

oh so it's like its local minimum and maximum?

Answer 20

Does that help John?

Answer 21

Yeah thanks a lot