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Locate all critical points of s(t) = (2 t  3)^(2) (8  2 t)^(3)?
 8 months ago
 8 months ago
Locate all critical points of s(t) = (2 t  3)^(2) (8  2 t)^(3)?
 8 months ago
 8 months ago

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PaynesdadBest ResponseYou've already chosen the best response.1
Ok is this a calc problem?
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.1
SO your critical points are max, min, and points of inflection, right?
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
critical points are x
 8 months ago

mathcalculusBest 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
 8 months ago

PaynesdadBest 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.
 8 months ago

SithsAndGigglesBest 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 \(s'(t)=0\).
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.1
That would locate your max and minimums but not your points of inflection. @SithsAndGiggles
 8 months ago

SithsAndGigglesBest 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.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
@SithsAndGiggles we used the product AND chain rule right?
 8 months ago

SithsAndGigglesBest ResponseYou've already chosen the best response.2
Product, chain, power (not necessarily in that order).
 8 months ago

SithsAndGigglesBest 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.
 8 months ago

PaynesdadBest 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.
 8 months ago

mathcalculusBest ResponseYou've already chosen the best response.0
@Paynesdad oh sorry, no i was only looking for the critical points.
 8 months ago

PaynesdadBest ResponseYou've already chosen the best response.1
Sounds like you have a good handle on this problem...Nice work @SithsAndGiggles and @mathcalculus
 8 months ago
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