The Hessian

Practice Questions

Linear Algebra › The Hessian

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1

Give the Hessian matrix for the function $f(x,y) = xy^{2}e^{x}$ .

2

Find the Hessian of the following function.

$f(x,y,z)=\frac{1}{2}xy^2+\ln(yz^2)+x^3$

3

$\begin{align*}&\text{Determine the Hessian, }H\text{, of the function}\&f(x,y)=20xy^{2}\end{align*}$

4

Give the Hessian matrix of the function $f(x, y) = \frac{1}{x^{2}y^{3}}$

5

$\begin{align*}&\text{Determine the Hessian, }H\text{, of the function}\&f(x,y,z)=6sin(6z)e^{(3x)}e^{(3y)}\end{align*}$

6

$f(x,y)= x^{2} - 3xy - y^{2}$

Use the Hessian matrix , if applicable, to answer this question:

Does the graph of have a local maximum, a local minimum, or a saddle point at ?

7

$\begin{align*}&\text{Determine the Hessian, }H\text{, of the function}\&f(x,y,z)=3\cdot 4^yz^{2}e^{(6x)}\end{align*}$

8

Let $f(x, y) =2^{x}3^{y}$ .

Find the Hessian matrix .

9

Let $f(x,y, z) = xy \cos z + xz \tan y$

Which of the following does not appear in the Hessian matrix of ?

10

Consider the function $f(x, y) = 2x \cos y - 2x$ .

Determine whether the graph of the function has a critical point at ; if so, use the Hessian matrix to identify as a local maximum, a local minimum, or a saddle point.

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