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mathcalculus
 one year ago
HELP please. Locate all critical points :
(The answers are to be points.
mathcalculus
 one year ago
HELP please. Locate all critical points : (The answers are to be points.

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tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Have you considered the 1st and 2nd derivatives?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0okay so i did this: s'(T)= 4(t3)^3 (t+2)^5+(t3)^4 5(t+2)^4(1)

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Very good, excepting the upper case "T" on the left hand side. It is generally considered bad form to change variables in the middle of the equation. Okay, what does that 1st derivative tell us?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0wait: it is 4(t3)^3(1)(t2)^5+(t3)^4 5(t2)(1)

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i am going to use product rule and chain rule.

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1It is not necessary to carry the (1). It is understood or unnecessary. Okay, you have managed a correct 1st derivative twice. Now, what does that tell us?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0then... 4(t3)^3 (t2)^5 +5(t3)^4 (t2)

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0yes but i still write it to be sure.. :/

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1To Luis_Rivera's "point", I think the intent is to report (a,b) rather than x = a.

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0now where im stuck is on the factoring part...

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0well we know we have to find the points.... in order to do that we must find x, so both are right.

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0@tkhunny now how do i move on after this?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1That's fine. I have no objection to carrying the (1) along if it helps you understand what you are doing. Time to break out your algebra skills. 4(t3)^3 (t+2)^5 +5(t3)^4 (t+2)^4 Common (t3)^3 (t3)^3[ 4(t+2)^5 +5(t3)(t+2)^4] Common (t+2)^4 s'(t) = (t3)^3 (t+2)^4 [4(t+2) +5(t3)] Okay, now what? Note: I'm not going to do that for you on the 2nd Derivative.

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.11) There is no (t2), it is (t+2). Please be more careful. 2) The common factor was (t+2)^4. This leaves one (t+2) in one term, since it started with (t+2)^5

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Right now, we're just playing with symbols. It is important to be able to do that, but it doesn't help much if we don't know what to do with all the nice little symbols when we are done playing with them. I ask again. What does the 1st derivative tell us?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0anyone like to help? let me hagning up thereee;/

mathmate
 one year ago
Best ResponseYou've already chosen the best response.0@mathcalculus when you work with a master, you would have to be attentive of what the question is about. If you don't understand the question, ask and ask again what he want to know from you. You are lucky to work with @tkhunny for the past halfan hour. If I have an advice at this point, make sure you understand the definition of "critical point" before proceeding, so you know what you're looking for!

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i've ACTUALLY been waiting..

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i do know the definition for critical point, what i needed help was on the factoring form..

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1You haven't answered my question, so I was beginning to wonder if you were still working on it.

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i calculated wrong. i needed to see where i made my mistake

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0@tkhunny yes i was working on it.

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0@tkhunny that determines the critical points. the derivative can;t = to zero.

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Fair enough. It helps if you tell me, so I don't give up on you. If s'(t) = 0, what does that tell us? (t3)^3 = 0 at t = 3 (t+2)^4 = 0 at t = 2 [4(t+2) +5(t3)] = 0 at t = 7/9 So, it appears s'(t) CAN be zero. What do we know when it is?

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1Maybe. Not if it is superseded by an inflection point. We must keep track. No conclusions until all the evidence is in.

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1gtg Up to pdpilot326 from here.

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1not necessarily y = x^3 has a derivative f'(0) = 0 but it's not a min nor max.

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1check this... http://tutorial.math.lamar.edu/Classes/CalcI/CriticalPoints.aspx

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0@pgpilot is it okay to move on from where i left off?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0s'(t) = (t3)^3 (t+2)^4 [4(t+2) +5(t3)]

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0@pgpilot326 thank you, i think I am understanding this better but i hate being asked questions like i'm some sort of mathematician..

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0the problem i has was factoring it.. now to find the critical points i know i have to look for x by setting it to zero after i find the derivative.

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1simplify in the brackets to better see the zero... \[[4\left( t+2 \right)+5\left( t3 \right)]=4t+8+5t15=9t7\] now you have all factors so any of them can be zero... \[s'\left( t \right)=\left( t3 \right)^{3}\left( t+2 \right)^{4}\left( 9t7 \right)\] so s'(t) = 0 if t = ?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0from there plug into original function and find the y's to each x

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1yes, you can also check the 2nd derivative or use a number line with your critical points and check to see which intervals are + or . this will tell you if you have a max, min or neither.

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1\[s′(t)=(t−3)^{3}(t+2)^{4}(9t−7)\] dw:1375838972632:dw so you should have a rel. max at 7/9 and a rel. min at 3

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0but for this questions they want the points...

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0i used the critical numbers and plugged into the orginal equation and i find it wrong.. it' seems wrong.

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1i understand... just giving you a bit extra.

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0(3,0),(2,0),(7/9,4033.09)

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0oh well thankyou for that.

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1it's not 7/9, it's 7/9...

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1no, 7/9 = 0.7777777777 to infinite and beyond...

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1oh, well then that's all good. why does it seem wrong?

mathcalculus
 one year ago
Best ResponseYou've already chosen the best response.0don't i use this critical number and plug it in?

pgpilot326
 one year ago
Best ResponseYou've already chosen the best response.1yes, you want s(7/9)

tkhunny
 one year ago
Best ResponseYou've already chosen the best response.1So, we're not going to pursue the points of inflection?
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