Question

for f(x)=(x^4+1)/(x^2) find any maximum, minimum, points of inflection, intervals where the function may be increasing or decreasing, concave up, or concave down. please help and show all steps!

Answer 1

Take derivative and set equal to zero to find max/min points.
Take 2nd derivative and set equal to zero to find inflection points.

Function is increasing when f' > 0, decreasing when f' < 0
Concave up when f'' >0, concave down when f'' < 0

Answer 2

Use quotient rule to find derivative

\[\frac{f}{g}' = \frac{f'g - fg'}{g^{2}}\]

Answer 3

A PDF solution with a plot is attached.