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chochko
 2 years ago
find the critical numbers
f(x)=x^4+4x^3+5
chochko
 2 years ago
find the critical numbers f(x)=x^4+4x^3+5

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

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

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

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

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

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

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

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

chochko
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1the next part is to differentiate it again :P to determine its nature

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

chochko
 2 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
 2 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
 2 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
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1max or min concave up => min concave down => max

chochko
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1well i googled; relative extrema and max/ min extrema is the same thing

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

Mimi_x3
 2 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
 2 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
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1i think i made a mistake; increasing \(f'(x)>0\)

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

Mimi_x3
 2 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
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1oh no no im getting tired @ParthKohli: may like to explain :)

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

Mimi_x3
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1Didn't notice the tag right there. :P

chochko
 2 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
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1What is the question again?

chochko
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1So it starts decreasing after 3.

chochko
 2 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
 2 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
 2 years ago
Best ResponseYou've already chosen the best response.1It's decreasing at f(5).

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

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

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

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

ParthKohli
 2 years ago
Best ResponseYou've already chosen the best response.1Damn... I've disabled the tag notifs.
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