italy-esame-di-stato 2024 Q5

italy-esame-di-stato · Other · esame-di-stato__matematica Stationary points and optimisation Determine parameters from given extremum conditions
5. Determine the polynomial function of fourth degree $y = p ( x )$ knowing that, in a Cartesian coordinate system, its graph satisfies the following conditions: -it is tangent to the $x$-axis at the origin; -it passes through the point $( 1,0 )$; -it has a stationary point at $( 2 , - 2 )$.
5. Determine the polynomial function of fourth degree $y = p ( x )$ knowing that, in a Cartesian coordinate system, its graph satisfies the following conditions:\\
-it is tangent to the $x$-axis at the origin;\\
-it passes through the point $( 1,0 )$;\\
-it has a stationary point at $( 2 , - 2 )$.\\