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a) For cubic curve that no stationary points. Its differentiated form has to have a discriminant of >0.
Differentiated form has to have b^2<4ac. Example would include:
y=4x^3-2x^2+3x
dy/dx=12x^2-4x+3
b^2 is less than 4ac
b) For a cubic curve with stationary points where x=2 and x=5.
Differentiated form must = 0 when x=2 and x=5 therefore
dy/dx=(x-2)(x-5)=0
=x^2-7x+10
integral of this equation will give us our function
(x^3)/3-(7x^2)/2+10x+c where c can be any real value)