Minimize

subject to

. The Lagrangian would be

and has partial derivatives

Setting each partial derivative to 0, we have

From the third equation, it follows that either

or

. In the second case, we arrive at a contradiction:

since both

and

must be non-negative, yet this would mean e.g.

. So it must be that

.
The first and second equations then tell us that


from which we obtain

.
Thus the points on the cone closest to (16, 6, 0) are

.
Answer:
a) x=7
b) x=4
c) x= 1/9
I hope this helps! Do you need more help?
Answer:
K=15
Step-by-step explanation:
Answer:
x² + 10x + 25
Explanation:
Before we begin, remember the following:
(a + b)(a + b) = (a + b)² = a² + 2ab + b²
Now, for the given we have:
(x + 5)(x + 5)
We can note that the two brackets are identical.
Therefore, we can apply the above rule as follows:
(x + 5)(x + 5) = (x + 5)²
= (x)² + 2(x)(5) + (5)²
= x² + 10x + 25
Hope this helps :)