chochko
find the critical numbers
f(x)=-x^4+4x^3+5
Delete
Share
This Question is Closed
ParthKohli
Best Response
You've already chosen the best response.
1
As they always say: find \(f'(x)\) and equate that to \(0\).
ParthKohli
Best Response
You've already chosen the best response.
1
@chochko What would \(f'(x)\) be here?
chochko
Best Response
You've already chosen the best response.
0
-4x^3+12x^2
chochko
Best Response
You've already chosen the best response.
0
ANd then?
ParthKohli
Best Response
You've already chosen the best response.
1
Well that's correct - now equate it to zero.
ParthKohli
Best Response
You've already chosen the best response.
1
Solve this equation:\[\rm 4x^3 + 12x^2 = 0\]
chochko
Best Response
You've already chosen the best response.
0
-4x^3+12x^2=0
ParthKohli
Best Response
You've already chosen the best response.
1
Yeah, I meant -4x^3 + 12x^2 = 0
chochko
Best Response
You've already chosen the best response.
0
sry my computer is really slow. Would you factor out a 4?
Yahoo!
Best Response
You've already chosen the best response.
1
Yu..
4x^2 ( x-3) = 0
4x^2 = 0
x = 0
x-3 = 0
x = 3
ParthKohli
Best Response
You've already chosen the best response.
1
Mine too, and you can factor 4x^2 out.
ParthKohli
Best Response
You've already chosen the best response.
1
Yep, and what Yahoo! said are the critical points. ;)
chochko
Best Response
You've already chosen the best response.
0
thank you but im not done . that is just one part..can you help yahoo or ParthKohli?
ParthKohli
Best Response
You've already chosen the best response.
1
Sure.
Mimi_x3
Best Response
You've already chosen the best response.
1
the next part is to differentiate it again :P
to determine its nature
ParthKohli
Best Response
You've already chosen the best response.
1
You guys must be in the same school.
ParthKohli
Best Response
You've already chosen the best response.
1
lol
chochko
Best Response
You've already chosen the best response.
0
using the second derivitive test which is -12x^2+24x=0 set to 0 to determine all relative extrema, indicating the x and Y values and wheteher is a max or a min. Help please
Mimi_x3
Best Response
You've already chosen the best response.
1
lol @ParthKohli: the next step is common sense.
@chochko: with the differentiataed function sub the \(x\) that you found in the first step if its a negative then its concave down => max.
if its concave up then => min
ParthKohli
Best Response
You've already chosen the best response.
1
Sorry, was on another question, and yeah - that's the way I was taught too.
chochko
Best Response
You've already chosen the best response.
0
so in -12x^2+24x Sub the x for the critical numbers and the result is the relative extrema? is that the Max and Min as well?
Mimi_x3
Best Response
You've already chosen the best response.
1
max or min
concave up => min
concave down => max
chochko
Best Response
You've already chosen the best response.
0
so which part is the relative extrema? i really suck at math btw?
Mimi_x3
Best Response
You've already chosen the best response.
1
well i googled; relative extrema and max/ min extrema is the same thing
chochko
Best Response
You've already chosen the best response.
0
f''(0)=0 min
f''(3)=-36 Max Is this correct?
Mimi_x3
Best Response
You've already chosen the best response.
1
i dont know; i dont have a calculator with me
but if its you have to check if it has a horizontal point of inflexion
chochko
Best Response
You've already chosen the best response.
0
Ok, so the intervals are the critical points right? where are they increasing and decreasing?
Mimi_x3
Best Response
You've already chosen the best response.
1
critical points are the stationary points on the curve since \(f(x)=0\)
you differentiate it twice to determine if its increasing or decreasing
increasing \(f''(x) >0\)
Mimi_x3
Best Response
You've already chosen the best response.
1
i think i made a mistake; increasing \(f'(x)>0\)
Mimi_x3
Best Response
You've already chosen the best response.
1
when the function is decreasing \(f'(x)<0\)
Mimi_x3
Best Response
You've already chosen the best response.
1
i mean you differetiate it once; to see if its increasing or decreasing
sorry; im sick
chochko
Best Response
You've already chosen the best response.
0
so using the f'(x)=0 and plug in 0 and 3 for x to find where f(x) is increasing or decreasing?
Mimi_x3
Best Response
You've already chosen the best response.
1
oh no no
im getting tired @ParthKohli: may like to explain :)
chochko
Best Response
You've already chosen the best response.
0
ok thanks a lot
chochko
Best Response
You've already chosen the best response.
0
@ParthKohli are you able to help me finish this one
Mimi_x3
Best Response
You've already chosen the best response.
1
I think I should explain; since Parth is hiding :P
\(f'(x) = 0\) you are finding the \(x\) values that is the STATIONARY point.
\(f'(x) >0\) is the \(x\) values were the function is INCREASING
\(f'(x)<0\) is where the function is DECREASING.
The second derivative is the deirivative of the derivative.
The curve \(y=f(x)\) is concave up when \(f''(x)>0\) and concve down when \(f''(x)<0\)
ParthKohli
Best Response
You've already chosen the best response.
1
Sry, back.
ParthKohli
Best Response
You've already chosen the best response.
1
Didn't notice the tag right there. :P
chochko
Best Response
You've already chosen the best response.
0
Increasing on ( -inf, 0) (0,3) then decreasing (3, inf)
idk if its correct?
ParthKohli
Best Response
You've already chosen the best response.
1
Well your \(\rm f'(x)\) function is \(\rm -4x^2 +12x \) and the function is stationary at x = 3,0.
ParthKohli
Best Response
You've already chosen the best response.
1
What is the question again?
chochko
Best Response
You've already chosen the best response.
0
State the intervas for which f(x) is increasing or decreasing
So i tested the values -1, 1, 4 And got
F'(-1)=16 inc
f'(2)=8 inc
f'(4)=-64 dec.
idk if its correct?
ParthKohli
Best Response
You've already chosen the best response.
1
That's right.
ParthKohli
Best Response
You've already chosen the best response.
1
So it starts decreasing after 3.
chochko
Best Response
You've already chosen the best response.
0
(-inf, 0) (0,3) increasing then (3, inf) decreasing
Are the intervals right?
ParthKohli
Best Response
You've already chosen the best response.
1
Let's test f'(-5).
f'(x) = -4x^2 + 12x
f'(-5) = -4(-5)^2 + 12(-5)
= -4(25) - 60
= -100 - 60 = -160
ParthKohli
Best Response
You've already chosen the best response.
1
It's decreasing at f(-5).
ParthKohli
Best Response
You've already chosen the best response.
1
The best way is to ask Wolfram for the graph. :)
chochko
Best Response
You've already chosen the best response.
0
huh? whos that?
ParthKohli
Best Response
You've already chosen the best response.
1
Enter your function and see its graph.
chochko
Best Response
You've already chosen the best response.
0
ok can you help me find the possible inflection points
chochko
Best Response
You've already chosen the best response.
0
@ParthKohli can you help just a lil bit left
ParthKohli
Best Response
You've already chosen the best response.
1
Sorry, back.
ParthKohli
Best Response
You've already chosen the best response.
1
Damn... I've disabled the tag notifs.