Question

The maximum value of the function f(x)= x^4 - 4x^3 + 6 on (1,4) is

Answer 1

can you find f'?

Answer 2

Yeah, f'(x) = 4x^3 - 12x^2

Answer 3

correct.

Answer 4

set f'=0

Answer 5

not, replace the f'(x) with 0.

Answer 6

and solve for x

Answer 7

I meant "now" replace

Answer 8

x= 0 and x= 3

Answer 9

Cool stuff but 0 isn't on the interval you are to look at right?

Answer 10

so we are to look at x=3

Answer 11

okay, right

Answer 12

Are you sure it is (1,4) and not [1,4] ?

Answer 13

I would like to verify x=3 will give us a max
so we could find f'' to make sure

Answer 14

Yeah it is brackets, I couldn't find the brackets on my keyboard sorry

Answer 15

So it should be [1,4] ?
then 1 and 4 would also be (automatically) included as your critical numbers

Answer 16

btw, [ ] should be below the + = on your keyboard

Answer 17

ah we are including 1 and 4 okay

Answer 18

Yeah, I get all that but the answer is 6, which not what we have as candidates yet

Answer 19

nice esp @idku :p

Answer 20

you need to plug in your endpoints

Answer 21

you have 4, 3, 1.

Answer 22

like @idku has suggested

Answer 23

plug them into the original function?

Answer 24

yes

Answer 25

plug your critical numbers into the f(x), and see which gives you the max output

Answer 26

(you can see that when you plug in 4 for x,
that:

(4)^4 - 4(3)^4 >>> 4^4 - 4^4 >>> 0

Answer 27

I meant something else

Answer 28

(4)^4 - 4(4)^3 >>> 4^4 - 4^4 >>> 0

Answer 29

so f(4) gives you 6 which is the highest out of the three so

Answer 30

yes, f(6) gives you 6, but you would still want to check the rest

Answer 31

I mean f(4)...sorry

Answer 32

yeah f(3) is -21 and f(1) is 3

Answer 33

yes, so then your absolute maximum is?

Answer 34

6?

Answer 35

Yes

Answer 36

I always thought your maximum was going to be a critical value... but it is the output not the critical value???

Answer 37

Yes, the maximum value is the y-value, the output.

Answer 38

How high the function can get

Answer 39

And not the x value that this height occurs.

Answer 40

Oh okay thanks so much...could you answer a couple more questions?

Answer 41

One more, I guess I can.

Answer 42

Shoot