italy-esame-di-stato 2025 Q4

italy-esame-di-stato · Other · esame-di-stato__matematica Tangents, normals and gradients Normal or perpendicular line problems
4. Given a function $g$, differentiable on $\mathbb { R }$ and such that $g \left( \frac { \pi } { 4 } \right) = g ^ { \prime } \left( \frac { \pi } { 4 } \right) = 2$, determine the equation of the normal line to the curve $y = g ( x ) \sin ^ { 2 } x$ at its point with abscissa $\frac { \pi } { 4 }$. 
4. Given a function $g$, differentiable on $\mathbb { R }$ and such that $g \left( \frac { \pi } { 4 } \right) = g ^ { \prime } \left( \frac { \pi } { 4 } \right) = 2$, determine the equation of the normal line to the curve $y = g ( x ) \sin ^ { 2 } x$ at its point with abscissa $\frac { \pi } { 4 }$.
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8