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anonymous
 5 years ago
Find all critical points of R(t)=3t+7715ln(t^23)
anonymous
 5 years ago
Find all critical points of R(t)=3t+7715ln(t^23)

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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0R' = 3 (30t)/(t^23) i think

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03t^2 30t 9  t^2 3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03(t^2 10 3) would be the top if I did it right....

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I Got R'=315/(t^23)(2t)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep, as long as thats just screen clutter and not a glaring error :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0add the parts like fractions, 3(t^2 3) 30t  t^2 3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry how did you get 3(t^23) on top?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0the top becomes a quadratic.... a fancy name for "highest power is a 2"

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0ok... you pretty much have the form: 30 3   now how do we add fractions togther? b

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have to have a common denominator?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0But if R'(t)=3 15 (2t)  (t^2 3)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0That would be 3  30t  (t^2  3)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.030t 3   is what we got right? (t^2 3)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0then to add the "fractions" mulitply the left part by: 3 t^23  x  right? 1 t^23

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0:) deriving...no problem.... fractions? ehhhh :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03t^2 30t 9  t^2 3

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0quadratic formula for the top to find the critical points...

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.05 + [sqrt(900  (4)(3)(9))]/6

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you familiar with the quadratic formula?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0good heres what I get: t = 5 + 2sqrt(63)/3

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Did you do quadratic formula of 3t^230t9?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep..... as long as I kept track of myself

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.030 sqrt(900(4)(3)(9))  +  6 6

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So 30 + sqrt(900+108)  6

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0we can simplify that by factoring out a 3 first.... sneaky little bugger it is :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.03(t^2 10t 3) now quad the left side

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.010 + sqrt(100 (4)(3)(1))  2

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.010 + sqrt(112)   same result, just easier to see 2 2

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you know how to test for min and max?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So those are the critical points? The neg and pos value from that?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0yep... those are the critical points. to see how they are behaving, you take a second derivative....derive the derivative.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I don't think I have to do that.

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you sure? its fun :) if you have to determine if they are MIN MAX or inflections, then we would, but if you just gotta find criticals, thats it.... dont forget to include the end points of the graph as well, they might be important

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Wow, thanks! Can you help me with one more?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0i dunno....... i feel a bout of stupidy brewing amongst me brain cells :) ........sure why not :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Find all critical points of P(t)=cos(4t)+392t

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Holy cow sorry my computer spazzed out

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0thats just the cosine function moved about.... should be rather simple to determine

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I have found P'(t) if that helps

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0P' = 4sin(4t)  2 right?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yes that's what I got

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0good, then we are either both genuises or idiots :) Ill go with genuisesss

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.00 = 4sins(4t) 2 solve for sin(4t)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0what does 4t have to equal for sin to be 1/2?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0there are 2 angles, that will satisfy this

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0what? you gotta have SOME idea.... its just a circle :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0sin(30) = 1/2 and sin(150) = 1/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0How do I figure the two angles that will satisfy that?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you can either remember back to trig that a 306090 triangle has sides of 12sqrt(3) and interpolate from that, OR use the sin inverse function on a calculator

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what from that tells me that 30 and 150 are what I'm looking for?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Sorry I want to understand

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0sin^1 will only give you one angle tho...30. You have to remember to cross over the yaxis to get to the other one...150

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.04t = 30 and 4t = 150 solve for t :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0might be better to use radians instead of degrees, half dozen of one or 6 of the other

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh! Okay thanks. Moving on

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0whoa where did that come from?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0what!!! you see a bee??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0No I mean the 4t=pi/6 and 4t=5pi/6

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Wait is that 30 degrees and 150 degrees in radians?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0:) there are a few ways to express angles. you can use degrees: 30 and 150 are degrees. OR you can use "radians" which measures the angle using the radius itself as a measuring stick. a circle is 360 degrees around OR 2pi radians pi/6 = 30 degrees 5pi/6 = 150 degrees

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0To get a number for "t" we should use radians :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0t = pi/24 t = 5pi/24 is what I come up with

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.030/4 or 150/4 depending on what your answers are looking for

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0t = pi/24 = .1309 or t = 5pi/24 = .6545

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0for degrees... t = 7.5 degrees or t = 37.5 degrees

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay. I have a question.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0usually before solving for t my professor asks "which quadrants is sin negative in" why did we not have to look for that in this problem?

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0sin(angle) = 1/2 sin is only positive in Q1 and Q2 .... no need to look any where else, unless you can think of a reason to..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay. That makes sense. Thank you sooo much!

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0when sin = 1/2, it puts a different value into the equation that is not a critical point

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0you are soooo welcome :)

amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0if you have any more questions, just start a new posting :)
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