Question

find the (absolute) maximum value of the function
f(x)=5x^2+x^3-x^4

Answer 1

@terenzreignz hey can u please help me i only need to understand this one

Answer 2

You need to differentiate it first, can you do that?

Answer 3

no i dont know any of this please

Answer 4

You don't know how to take a derivative?

Answer 5

f'(x)=-4x^3+3x^2+10x this it

Answer 6

Oh okay, you had me worried there ^_^
Now, equate this to zero, and solve for x.
\[\Large -4x^3 +3x^2 +10x =0\]
You should get three values...

Answer 7

because i only get 12

Answer 8

Solving for x?
That's intermediate Algebra, isn't it?

Answer 9

no i mean -1.25

Answer 10

Okay, how did you get that?

Answer 11

factoring

Answer 12

True, but there ARE two other solutions...

Answer 13

2 and 0

Answer 14

Okay, good. Now, if your function has any maxima, it has to be at a point where the derivative was zero...
Now... compare them... plug in zero, -1.25, and 2 to your function, and see which one gives you the largest value...

Answer 15

2=12
-1.25=3.417
0=0

Answer 16

So which is biggest?

Answer 17

2

Answer 18

So its absolute maximum is...?
(It's the largest value the function attains)

Answer 19

And it's not 2 = 12, silly...
it's f(2) = 12

Answer 20

ok so is it 2 or 12 because they both are my answers choices

Answer 21

Which do you think?
What's the highest value the function attains...

Answer 22

12

Answer 23

Well then ;)

Answer 24

thank u so much :)