Question

Can you help me solve this? http://screencast.com/t/XZ7n99PHIz

I am stuck at finding the decreasing and increasing intervals.

I cant solve the inequality that pops up

Answer 1

for this question, you need take derivative to consider whether f increasing or decreasing and second derivative to know whether concave up or down

Answer 2

try to find the decreising for the derivative, its unsolvable

Answer 3

why? try once, take derivative , let me know the result. ok?

Answer 4

derivative = 4x^3 - 10x^2 + 18x i cant solve this

Answer 5

factor 2x out

Answer 6

Dude trust me I am to the finishing steps on this it cant be solved, have you tried to solve it?

Answer 7

of course, you must solve it to get the critical point to consider the decreasing or increasing. that's the only way to do.

Answer 8

can you please try and tell me if you can solve it

Answer 9

please?

Answer 10

at least, I have x =0 ok?

Answer 11

yea

Answer 12

the second and third one is undefined when they are complex numbers, right? so, just have one critical point, that's ok ,too

Answer 13

why not?

Answer 14

can I actually do this?

Answer 15

hey , I recheck, you take wrong derivative, it's is 4x^3 -15x^2 +18x hhhhmmmm

Answer 16

I think the only critical point is at x=0

Answer 17

@Christos am I right?

Answer 18

a ha,,,, so,???

Answer 19

And yes, that's the derivative I have
@Loser66

Answer 20

hehehe,,, redo, friends!!!

Answer 21

So we need to check the sign of the derivative when x<0 and when x>0
Those are the increasing and decreasing intervals

Answer 22

perfect, let bingbing1995 continue, is it ok, friends??

Answer 23

@Christos Is this OK with you?

Answer 24

yes sure np!

Answer 25

:)

Answer 26

so, can I leave?

Answer 27

if you want to its ok by all means :)

Answer 28

@Christos Do you see what I did?

Answer 29

yes I know about the intervals I just cant solve the inequality

Answer 30

You don't need to solve the inequality
Plug in different x-values to the equation for the derivative

Answer 31

For instance, find f'(1)

Answer 32

Is it positive or negative?

Answer 33

negative

Answer 34

You sure?

Answer 35

positive sorry!

Answer 36

So if the derivative is positive, the function is...

Answer 37

increasing

Answer 38

Right. And since there aren't any critical points to the right of x=0, the function is increasing for all of x>0. Make sense?

Answer 39

but we have a 3rd degree expression that means 3 roots

Answer 40

Not necessarily

Answer 41

roots/solutions

Answer 42

Some of them might be complex roots. Consider
\[y=x ^{2}+1\]
You would expect two roots, but look at the graph.

Answer 43

There are no values of x where y=0, so there are no real roots.

Answer 44

Does that make sense?

Answer 45

I am kinda confused :(

Answer 46

so why this applies for our specific expression?

Answer 47

OK, try this.
Try to solve
\[x^2+1=0\]

Answer 48

I see but why it has to be like this with our derivative

Answer 49

Do you have a calculator where you can graph the derivative? Try that.

Answer 50

I am afraid I won't be allowed a calculator at the final exams which is why I need to learn how to figure it out without the graph

Answer 51

That's OK. I can explain it to you more easily if you see the graph first.

Answer 52

alright sec

Answer 53

How many times and where does the graph cross the x-axis?

Answer 54

one time

Answer 55

Right. So, there's only one place where the graph of f(x) changes from decreasing to increasing.

Answer 56

How did you know how the graph looks like just by looking at the expression?

Answer 57

Well, you know there's a root at x=0 because you can factor out an x from the derivative. \[f'(x) = x(4x^2-15x+18)\]
There aren't any x-values that make the other part of the equation equal to zero. Do you want me to explain how I know that without the graph?

Answer 58

Remember the quadratic formula:
\[x=(-b \pm \sqrt{b^2-4ac})/(2a)\]
You can't take the sqaure root of a negative number, right? So if \[b^2-4ac\] is less than zero, there's no solution to the equation.
For our equation, \[4x^2-15x+18\] \[b^2-4ac=-63\]
Thus, there are no x-values that make that expression zero.

Answer 59

Are you still confused?

Answer 60

:)

Answer 61

+Medal Fanned thank you!!

Answer 62

But does it make sense to you? the upshot of it all is that you can check whether an equation has a solution by plugging in the coefficients to b^2-4ac.

Answer 63

Yes yes I understood the whole of it

Answer 64

Yay!!!!!

Answer 65

::D