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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!

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1 Answer 1

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If $f(x)=ax^3+bx^2$ passes through $(-1,1)$ then you have one equation: $ -a+b = 1$

and if you take the second derivative you get $f''(x)=6ax+2b$ you have another equation that you can form given the information you have, do you know how to continue now?

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  • $\begingroup$ Thanks alot! I got it from there! I just had a lot of (false) options and didn’t know which to choose in order to get a/b out :/ $\endgroup$
    – SOMI
    Oct 3, 2017 at 1:13
  • $\begingroup$ No problem, feel free to tick my question if it helped :) $\endgroup$
    – bigfocalchord
    Oct 3, 2017 at 1:14

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