help? optimization ?

Question

Answer 1

(3)

Step 1:

Let the two non negative numbers be and .

The sum of two numbers is .

Product of one number and square of other number is .

.

The product of the two numbers is maximum, find the two number by equating its first derivative to zero.

Now verify the maximum value using second derivative test.

Substitute  in above equation.

So the function has maximum at .

Substitute .

So the function has minimum at .

So substitute .

Therefore the two non negative numbers are and .

Solution :

Two non negative numbers are and .

Answer 2

(4)

Step 1:

The function is and point is .

Graph:

Graph the function and point .

Now observe the graph :

The points of a function that are closer to point are .

Solution:

The points closest to the point are .