Question: how to find turning points, critical points and inflection points

Hi guys,

I have some information about function f(x)=x^2+y(1-x)^3/4 where x domain is [0,1] and y is a parameter but i can not obtained this information with maple.

I know function f(x) for y>1.4266 is monotically decreasing and there is no turning points,(actually i can compute infection points of above function: y=1.4266 and x=4/5 )

I know function for 1.4266>y>1.0144 has two turning points a minimum for x<4/5 and a maximum for x>4/5 , but i dont know how y=1.0144 is calculated and what is the nature of this point !!! and how this relates to x><4/5 !

I know fucntion for y<1.0144 has to two turning points that the global maximum of function happens at x<0.97702, but also i can not compute 1.0144 and how this relates to x<0.97702 !!


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