Question

Determine if the following functions are concave, convex or neither. (d) $f(x, y) := 3x + y^2$. (c) $f(x, y) := x^{1/2}y^{1/2}$ (on $\mathbb{R}^2_{++}$). (f) $f(x, y) := x^3 - x^2 - y^2$.

          Determine if the following functions are concave, convex or neither.
(d) $f(x, y) := 3x + y^2$.
(c) $f(x, y) := x^{1/2}y^{1/2}$ (on $\mathbb{R}^2_{++}$).
(f) $f(x, y) := x^3 - x^2 - y^2$.

Determine if the following functions are concave, convex or neither.
(d) f(x, y) := 3x + y^2.
(c) f(x, y) := x^1/2y^1/2 (on ℝ^2++).
(f) f(x, y) := x^3 - x^2 - y^2.

Added by Derrick T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Imogen Dell

Step 1

Taking the second-order partial derivatives, we get: f_xx = 2 f_yy = 2 Since both second-order partial derivatives are positive, we can conclude that the function is convex. (c) f(x, y) = âˆš(1/2|y|): To determine if this function is concave or convex, we need Show more…

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