Question

Identify the local maximum value for the function f (x) = x^6 - 6x^4 + 5, using the first derivative test.

Answer 1

what do you get for the derivative?

Answer 2

6x^5-24x^3

Answer 3

similar to last one yes? take the derivative. factor. find the zeros. check the sign

Answer 4

is that right?

Answer 5

thats good

Answer 6

it is cooked up to factor easily. and so easy to find the zeros yes it is right. factor now

Answer 7

now to zero it out factor out what it has in common

Answer 8

Ummm.. Im not sure how to do it but ill give it a shot.. :/ 6(x^5-4x^3). Is that right?

Answer 9

Is this correct or am I wrong?

Answer 10

can factor out a lot more than that. as in previous example

Answer 11

i'll give you a hint. it is
\[6x^3(x^2-4)\]

Answer 12

okay. I got this far with your help.. I have no clue as to how to go to the next step

Answer 13

set the derivative = 0 and solve

Answer 14

you will get 3 zeros. name them

Answer 15

\[6x^{3}\ +(x^{2}-4) = 0\]

Answer 16

hello? pleae dont make me sad :(

Answer 17

6x^5 -24x^3 ; factor out the 6 and the x^3

6x^3 (x^2 - 4) = 0 ; we can factor it again or just realize the +- 2 give the same results

so when x = -2, 0, 2 we have critical points

Answer 18

6x^3 (x-2) (x+2)

when we plug in a -3 we get; -.-.- = -
when we plug in a -1 we get; -.-.+ = +
when we plug in a 1 we get; +.-.+ = -
when we plug in a 3 we get; +.+.+ = +

<.........-2..........0...........2.........>
- + - +

ride this like a roller coaster now, from left to right

at -2 we go down then up, thats a minimum
at 0 we go up then down; that a maximum
at 2 we go down then up; that a minimum.

http://www.wolframalpha.com/input/?i=x^6+-+6x^4+%2B+5