How do you determine the concavity for #f(x)=x^4# ?

1 Answer
Wataru
Sep 7, 2014

#f(x)=x^4# is concave upward on #(-infty,+infty)#.

By taking the derivatives,
#f'(x)=4x^3#
#f''(x)=12x^2 geq 0#,
which means that #f'# is increasing on #(-infty,+infty)#,
which means that #f# is concave upward on #(-infty,+infty)#.

Related questions
See all questions in The special case of x⁴
Impact of this question
2588 views around the world
You can reuse this answer
Creative Commons License