Given

subject to the constraint

Let

.
The gradient vectors of

and

are:

and

By Lagrange's theorem, there is a number

, such that


It can be seen that

has local extreme values at the given region.
D.
f(x) can be written as (x+2)(x-2)(x-1)
by using difference of two squares to expand x^2 - 4 whch yields 3 x intercepts
similarly, k(x) can be written as
x(x+5)(x-5) which also yields 3
x intercepts (0,-5, and 5)
Only two integers i think, 7 and -7