Let , where and are real parameters. Find all ordered pairs such that is concave down…

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

F_{m,n}(x)=m x^{4}+n x^{2}+1

, where

m

and

n

are real parameters. Find all ordered pairs

(m,n)

such that

F_{m,n}

is concave down on the entire real line.