spain-selectividad 2024 QB.2

spain-selectividad · Other · selectividad__matematicas-II_modelo 2.5 marks Stationary points and optimisation Find critical points and classify extrema of a given function
Given the real function of a real variable $f ( x ) = x - \frac { 4 } { ( x - 1 ) ^ { 2 } }$, it is requested:
a) ( 0.75 points) Find the domain of definition of $f ( x )$ and determine, if they exist, the equations of the asymptotes of its graph.
b) (1 point) Determine the relative extrema of the function, as well as its intervals of increase and decrease.
c) ( 0.75 points) Calculate the equation of a tangent line to the graph of $f ( x )$ that is parallel to the line with equation $9 x - 8 y = 6$.
Given the real function of a real variable $f ( x ) = x - \frac { 4 } { ( x - 1 ) ^ { 2 } }$, it is requested:

a) ( 0.75 points) Find the domain of definition of $f ( x )$ and determine, if they exist, the equations of the asymptotes of its graph.

b) (1 point) Determine the relative extrema of the function, as well as its intervals of increase and decrease.

c) ( 0.75 points) Calculate the equation of a tangent line to the graph of $f ( x )$ that is parallel to the line with equation $9 x - 8 y = 6$.