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Let f be the function defined by f(x)=3x^5  5x^3 +2
(a) On what intervals is f increasing?
(b) On what intervals is the graph of f concave upward?
(c) Write the equation of each horizontal tangent line to the graph of f.
 one year ago
 one year ago
Let f be the function defined by f(x)=3x^5  5x^3 +2 (a) On what intervals is f increasing? (b) On what intervals is the graph of f concave upward? (c) Write the equation of each horizontal tangent line to the graph of f.
 one year ago
 one year ago

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lilfayfayBest ResponseYou've already chosen the best response.0
do first derivative test?
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
@Goten77 ok for first derivative i got 15x^4  15x^2
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
k thats right now factor it
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
set each = to 0 and get critical points dw:1358134445508:dw but also find where x never exist.. but it always does so ignore that part
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
now set up the critical points to test for when its positive and negative and you use the 1st derivative when plugging in theese valuesdw:1358134521331:dw u just use values in between the numbers
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
so thats part a when its increasing/decreasing.... also part c is just the graphs of y = 0 , 1, +1 since those are the 3 horizontal tangents
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
part b is 2nd derivative test
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
for part a.) is it (infinity,1) & (1,infinity)
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
ok for part b.) i got x=0, and \[\pm \frac{ \sqrt{2} }{ 2 }\]
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
dw:1358135162509:dw hmm you number works to...
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
then i do the SDT? (Second Derivative Test)?
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
well there the same i meant XD
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
yes now you test those numbers between/around them
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
ok, how do i do part c.)? o:
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
so um heres part bdw:1358135773604:dw
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
hmm the squareroot number is very small....
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
for b.) did u get \[(\frac{ \sqrt{2} }{ 2 }, \infty)\]
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
oh i keep on thinking about point of inflection <.<
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
dw:1358128938034:dw o.O
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
is that drawing seem right? :\
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
yes your right... its only concave up on that last interval
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
so how do i do part c.) again sorry..
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
wait so my part b.)was wrong?
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
so heres what the graph looks like dw:1358136607164:dw
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
aah i meant to say for part (c)
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
k everything is right now.... i just got part letters mixed up
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
so how do ido part c.)
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
......u kno what i meant... that entre paragraph just now is part C
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
oh i said it kinda wrong earlier i meant part Cis when f(x)= 1,0,1 meaning plug those 3 values into the original function and thats when the graph has a tangent lind so then you get y= 4 y= 2 y= 0 and thats when the graph has the horizontal tangents the x values of 1,0,1 came from the 1st derivative test since those are the critical points meaning where the derivative = 0
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
ah ok ty so for part c.) i got y=2x+2
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
yeah it says write the equation
 one year ago

Goten77Best ResponseYou've already chosen the best response.1
k so the 1st derivative gives us critical points meaning where the slope = 0 also meaning at those points on the original graph is where it has a horizontal tangent..... so taht means the horizontal tangents are in the form of y = # and thats it so our critical points were 1 0 and 1 plug those into the original equasion and get y= 4 y= 2 y= 0 and thats it .. those are your 3 horizontal tangents
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
ohso my answer waswrong xx
 one year ago

lilfayfayBest ResponseYou've already chosen the best response.0
@Goten77 canu help me with another 2 more pls? ^^
 one year ago
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