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mathcalculus
Group Title
Locate all critical points of s(t) = (2 t  3)^(2) (8  2 t)^(3)?
 one year ago
 one year ago
mathcalculus Group Title
Locate all critical points of s(t) = (2 t  3)^(2) (8  2 t)^(3)?
 one year ago
 one year ago

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Paynesdad Group TitleBest ResponseYou've already chosen the best response.1
Ok is this a calc problem?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@Paynesdad
 one year ago

Paynesdad Group TitleBest ResponseYou've already chosen the best response.1
SO your critical points are max, min, and points of inflection, right?
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
critical points are x
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
we have to solve for x... to find the y's and that gives us our point
 one year ago

Paynesdad Group TitleBest ResponseYou've already chosen the best response.1
Right but when the question says critical points...In calculus that is usually the maximum, minimum an/or points of inflection.
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.2
\[s(t)=(2t3)^2(82t)^3\\ \Rightarrow~s'(t)=4(2t3)(82t)^36(2t3)^2(82t)^2\\ \Rightarrow~s'(t)=(2t3)(82t)^2\left[4(82t)6(2t3)\right]\\ \Rightarrow~s'(t)=(2t3)(82t)^2(5020t)\] It should be fairly easy to find when \(s'(t)=0\).
 one year ago

Paynesdad Group TitleBest ResponseYou've already chosen the best response.1
That would locate your max and minimums but not your points of inflection. @SithsAndGiggles
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.2
@Paynesdad, usually when a problem asks for critical points, it's referring to the critical points of \(f(x)\). Points of inflection for \(f(x)\) are critical points of \(f'(x)\), not \(f(x)\), so I would think that's the assumption to be used here.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@SithsAndGiggles we used the product AND chain rule right?
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.2
Product, chain, power (not necessarily in that order).
 one year ago

SithsAndGiggles Group TitleBest ResponseYou've already chosen the best response.2
@Paynesdad, but that doesn't mean critical points can't be inflection points. Depends on the function.
 one year ago

Paynesdad Group TitleBest ResponseYou've already chosen the best response.1
Correct .. I just wanted to know if she would need to go on and get the 2nd derivative to find the points of inflection as well or just the first derivative critical points.
 one year ago

mathcalculus Group TitleBest ResponseYou've already chosen the best response.0
@Paynesdad oh sorry, no i was only looking for the critical points.
 one year ago

Paynesdad Group TitleBest ResponseYou've already chosen the best response.1
Sounds like you have a good handle on this problem...Nice work @SithsAndGiggles and @mathcalculus
 one year ago
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