Quiz Chapter 09.02: Newton’s Method – Holistic Numerical Methods

1. Which of the following is NOT required for using Newton’s method for optimization?

The lower bound for search region.

Twice differentiable optimization function.

The function to be optimized.

A good initial estimate that is reasonably close to the optimal.

2. Which of the following statements is INCORRECT?

If the second derivative at

x_{i}

is negative, then

x_{i}

is a maximum.

If the first derivative at

x_{i}

is zero, then

x_{i}

is an optimum.

x_{i}

is a minimum, then the second derivative at

x_{i}

is positive.

The value of the function can be positive or negative as any optima.

3. For what value of $x$ , is the function $x^{2} - 2x - 6$ minimized?

0

1

5

3

4. We need to enclose a field with a fence. We have $500$ feet of fencing material with a building on one side of the field where we will not need any fencing. Determine the maximum area of the field that can be enclosed by the fence.

x=125, \, y=250

x=450, \, y=200

x=125, \, y=100

x=200, \, y=150

5. A rectangular box with a square base and no top has a volume of $500$ cubic inches. Find the length, $l$ of the edge of the square base and height, $h$ for the box that requires the least amount of material to build. Conduct two iterations using an initial guess of $l=5$ in.

Base edge length is

10.00

and height is

5.00

Base edge length is

9.17

and height is

6.00

Base edge length is

9.00

and height is

6.17

Base edge length is

10.00

and height is

10.00

6. A rectangular box with a square base with no top has a surface area of $108$ ft². Find the dimensions that will maximize the volume. Conduct two iterations using an initial guess of $l=3$ ft.

Base edge length is

4.15

and height is

4.85

Base edge length is

6.15

and height is

2.85

Base edge length is

6.00

and height is

3.00

Base edge length is

3.85

and height is

6.15