Question

What is the maximum number of relative extrema contained in the graph of this function: f(x)=3x^4-x^2+4x-2

Answer 1

hint: take the derivative of the function. then examine how many zeros that function can have, namely the max number of real zeros. that will be your answer.

Answer 2

Can you help?

Answer 3

what's the dreivative?

Answer 4

derivative

Answer 5

f(x)=12x^3-2x+4

Answer 6

all right. what degree polynomial is the derivative?

Answer 7

cubic

Answer 8

how many zeros will it have?

Answer 9

10?

Answer 10

really? have you heard of the fundamental theorem of algebra?

Answer 11

Yeah? it has at least one complex root

Answer 12

http://www.mathsisfun.com/algebra/fundamental-theorem-algebra.html

have a look at this...

Answer 13

so 3

Answer 14

@pgpilot326 where'd you go!

Answer 15

right here... great. does that make sense?

Answer 16

Yeah,so how do I find max number of relative extrema

Answer 17

each relative extrema will occur at a zero of the derivative function. so if your function is a polynomial then the max number will be 1 less than it's degree.

Answer 18

So the max number is 3?

Answer 19

yep and the minimum number is 1. that's because when a polynomial has real coefficients, complex roots occur in conjugate pairs. since 3 is the max, 3-2 = 1 would be the min. (number of relative extrema won't be below 0).

Answer 20

Ok that makes a lot of sense! Would you mind helping on one more? It is pretty easy identifying a polynomial from a multiple choice list. Just be check my answer

Answer 21

sure

Answer 22

WHich is a polynomial:
f(x)=4/x - 11x^2
f(x)= -2.1^7+3x^2+17/2 x ---- my answer
f(x)= -1/5x^2 +4.5x + 2^x
f(x)= -3x^4+8x^2-2sqrtx + 1

Answer 23

a polynomial must have non-negative, integer exponents.

Answer 24

Ok my answer is correct then

Answer 25

so in your answer, is the last term \[\frac{ 17 }{ 2x }\text{ or }\frac{ 17 }{ 2 }x\]

Answer 26

the second one

Answer 27

good

Answer 28

Thanks!

Answer 29

you're welcome!