I stumbled upon this exercise in which the function f(x)=ax^3 +bx^2 is given and it is asked to determine a and b for when the function crosses (-1,1) and has an inflection point at x=0.5
As far as I understood I have the second derivative which is f”(0.5)= 6*0.5*a+b= 0 and have to create some sort of system to get either a or b but I can’t figure out how to do this exactly.
P.s. sorry for the sloppy formulas but I am typing this from my phone.
Thanks in advance!