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burhan101
Group Title
Determine and classify all critical points of each function on the interval 4<x<4
f(x) = x⁴4x³
 one year ago
 one year ago
burhan101 Group Title
Determine and classify all critical points of each function on the interval 4<x<4 f(x) = x⁴4x³
 one year ago
 one year ago

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johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.0
Critical points are found via taking the first derivative of the function...and setting it = to 0 So what is \[\frac{ d }{ dx }x^44x^3\]
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
0=4x²(x3)
 one year ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.0
One step ahead of me...so you will have 2 critical points.. being...?
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
0 and 3 ?
 one year ago

johnweldon1993 Group TitleBest ResponseYou've already chosen the best response.0
That would be correct...Now do you have to classify if they are a max or a min or an inflection point?
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
How do i find that out?
 one year ago

Loser66 Group TitleBest ResponseYou've already chosen the best response.0
plug them into the original function and calculate its value. f(0) =? and f(3)=? compare them to give out the answer
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
(3, 27)
 one year ago

Loser66 Group TitleBest ResponseYou've already chosen the best response.0
ok, between them, which one is bigger? the bigger is local max, the smaller is local min. right?
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
what do you mean which one :S
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
like between (x,y)
 one year ago

Loser66 Group TitleBest ResponseYou've already chosen the best response.0
for your problem, so far you have 4 critical points, 4, 0, 3, 4, just plug them into the original function and make conclusion. done.
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
where did 4 and 4 come from ?
 one year ago

oldrin.bataku Group TitleBest ResponseYou've already chosen the best response.2
$$f(x) = x^44x^3\\f'(x)=4x^312x^2=4x^2(x3)\\4x^2(x3)=0\implies4x^2=0,x3=0$$... so we conclude \(x=0\) and \(x=3\) are our critical points. Both lie in our interval so classify them.
 one year ago

oldrin.bataku Group TitleBest ResponseYou've already chosen the best response.2
@burhan101 they're our endpoints, which you'd want to test when finding *absolute* extrema. @Loser66 had a minor misunderstanding
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
@oldrin.bataku what do i do with these points now?
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
plug them into f(x)?
 one year ago

oldrin.bataku Group TitleBest ResponseYou've already chosen the best response.2
@burhan101 no you want to check the second derivative:$$f''(x)=12x^224x=12x(x2)\\f''(0)=0\\f''(3)=12(3)=36>0$$... so our derivative is increasing near \(x=3\) meaning \(x=3\) is a relative minimum; since our derivative is neither increasing nor decreasing near \(x=0\) we find it's neither! (hence the even multiplicity)
 one year ago

burhan101 Group TitleBest ResponseYou've already chosen the best response.0
why are we plugging in 3 ?
 one year ago
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