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How to sketch the graph of f(x)=x^2(x^24) including the inflection point?
 2 years ago
 2 years ago
S Group Title
How to sketch the graph of f(x)=x^2(x^24) including the inflection point?
 2 years ago
 2 years ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.2
start with \[y=x^2(x2)(x+2)\] so you see that you have 3 zeros, at x =2,x=0,x=2
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
the zero at x = 0 has multiplicity 2, so the graph will touch the x  axis there but not cross it
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
to find the point of inflection you need the second derivative, \[f(x)=x^44x^2\] \[f'(x)=4x^38x\] \[f''(x)=12x^28\] set equal to zero and solve
 2 years ago

S Group TitleBest ResponseYou've already chosen the best response.0
My main question is that, when i find the inflection point I put square root of 2/3 into the original formula and i get 20/3 right?
 2 years ago

S Group TitleBest ResponseYou've already chosen the best response.0
And this point can not be on the graph, this makes me confused
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
yes, for the second coordinate you evaluate the function at \[\sqrt{\frac{2}{3}}\]
 2 years ago

S Group TitleBest ResponseYou've already chosen the best response.0
yes, so I should get 2 inflection points
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
it must be on the graph, plug in the x, find the y
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
right \[\pm\sqrt{\frac{2}{3}}\]
 2 years ago

S Group TitleBest ResponseYou've already chosen the best response.0
so when I plug I get  20/3
 2 years ago

fazna Group TitleBest ResponseYou've already chosen the best response.0
for point of inflection we need only to equate first derivative of f(x) to 0.not the second
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
actually it is the second first derivative gives relative max or min
 2 years ago

S Group TitleBest ResponseYou've already chosen the best response.0
it should be plugged in the original formula, right?
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
yes, original function you have the x, you want the y
 2 years ago

S Group TitleBest ResponseYou've already chosen the best response.0
But in the end my inflection point comes up to be ( square root of 2/3 ;  20/3) and (square root of 2/3 ;  20/3) and my minimum points are (2;4) and (2;4) and it seems that the point of inflection cant be on the graph
 2 years ago

fazna Group TitleBest ResponseYou've already chosen the best response.0
but im sure that i can get the points of inflection from first derivative,not the second
 2 years ago
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