Question

Find the relative extrema of the function, if they exist. f(x) x2 + 1 Relative minimum at (0, -5) O No relative extrema exist Relative maximum at (0.-5) O Relative maximum at (0,5)

Answer 1

We have the expression:

`f(x)=(-5)/(x^2+1)`

In orde to determine it's relative maximum and minimum, we operate as follows:

`f^(\prime)(x)=(10x)/((x^2+1)^2)`

When we equal x to 0, we will have the point (0, -5).

And replacing values near 0, we will have that before 0 decreases and after 0 increases, from this, we have that the point (0, -5) is a relative minimum.