A community for students.
Here's the question you clicked on:
 0 viewing
chochko
 3 years ago
find the critical numbers
f(x)=x^4+4x^3+5
chochko
 3 years ago
find the critical numbers f(x)=x^4+4x^3+5

This Question is Closed

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1As they always say: find \(f'(x)\) and equate that to \(0\).

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1@chochko What would \(f'(x)\) be here?

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Well that's correct  now equate it to zero.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Solve this equation:\[\rm 4x^3 + 12x^2 = 0\]

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Yeah, I meant 4x^3 + 12x^2 = 0

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0sry my computer is really slow. Would you factor out a 4?

Yahoo!
 3 years ago
Best ResponseYou've already chosen the best response.1Yu.. 4x^2 ( x3) = 0 4x^2 = 0 x = 0 x3 = 0 x = 3

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Mine too, and you can factor 4x^2 out.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Yep, and what Yahoo! said are the critical points. ;)

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0thank you but im not done . that is just one part..can you help yahoo or ParthKohli?

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1the next part is to differentiate it again :P to determine its nature

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1You guys must be in the same school.

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0using 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
 3 years ago
Best ResponseYou've already chosen the best response.1lol @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
 3 years ago
Best ResponseYou've already chosen the best response.1Sorry, was on another question, and yeah  that's the way I was taught too.

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0so 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
 3 years ago
Best ResponseYou've already chosen the best response.1max or min concave up => min concave down => max

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0so which part is the relative extrema? i really suck at math btw?

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1well i googled; relative extrema and max/ min extrema is the same thing

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0f''(0)=0 min f''(3)=36 Max Is this correct?

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1i 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
 3 years ago
Best ResponseYou've already chosen the best response.0Ok, so the intervals are the critical points right? where are they increasing and decreasing?

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1critical 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
 3 years ago
Best ResponseYou've already chosen the best response.1i think i made a mistake; increasing \(f'(x)>0\)

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1when the function is decreasing \(f'(x)<0\)

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1i mean you differetiate it once; to see if its increasing or decreasing sorry; im sick

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0so using the f'(x)=0 and plug in 0 and 3 for x to find where f(x) is increasing or decreasing?

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1oh no no im getting tired @ParthKohli: may like to explain :)

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0@ParthKohli are you able to help me finish this one

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1I 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
 3 years ago
Best ResponseYou've already chosen the best response.1Didn't notice the tag right there. :P

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0Increasing on ( inf, 0) (0,3) then decreasing (3, inf) idk if its correct?

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Well your \(\rm f'(x)\) function is \(\rm 4x^2 +12x \) and the function is stationary at x = 3,0.

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1What is the question again?

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0State 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
 3 years ago
Best ResponseYou've already chosen the best response.1So it starts decreasing after 3.

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0(inf, 0) (0,3) increasing then (3, inf) decreasing Are the intervals right?

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Let's test f'(5). f'(x) = 4x^2 + 12x f'(5) = 4(5)^2 + 12(5) = 4(25)  60 = 100  60 = 160

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1It's decreasing at f(5).

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1The best way is to ask Wolfram for the graph. :)

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Enter your function and see its graph.

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0ok can you help me find the possible inflection points

chochko
 3 years ago
Best ResponseYou've already chosen the best response.0@ParthKohli can you help just a lil bit left

ParthKohli
 3 years ago
Best ResponseYou've already chosen the best response.1Damn... I've disabled the tag notifs.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.