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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