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)#.

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