PLS HELP!! Mr. Holmgren is the band director at school. He asks
students to record how often they practiced the week
before a concert. The dot plot shows the data he has
recorded.
Time Spent Practicing
...
6
2 3
5
Number of days
What unit of measure is used in the study?
A. Number of students
O B. Weeks
O C. Number of observations
O D. Days
PREVIOUS

Days

Step-by-step explanation:

I'd say Days

See steps below

Step-by-step explanation:

The function  

is a particular case of the general Rosenbrock’s Function.

a)  

Since  

for all the values of x and equals 0 when x=1 and

for all the values of y and equals 0 only when y=1, we conclude that (1,1) is a minimum.

On the other hand,

f(x,y)>0 for (x,y) ≠ (1,1) so (1,1) is a global minimum.

b)

To confirm that this function is not convex, we will be using the following characterization of convexity

“f is convex if, and only if, the Laplace operator of f for every (x,y) in the domain of f”

Given that the domain of f is the whole plane XY, in order to prove that f is not convex, we must find a point (x,y) at where the Laplace operator is < 0.

The Laplace operator is given by

Let us compute the partial derivatives

and

we have then

if we take (x,y) = (0,1)

hence f is not convex.