Question is the attached file.

The critical points are 12 and 0.

Step-by-step explanation:

We have that the critical numbers are those values that result from equating the derivative of a function to zero. Also called roots or zeros of the derived function.

IF f is defined in x, it will be said that a is a critical number of f if f '(x) = 0 or if f is not defined in x.

Now the function is:

f (x) = x ^ 2 / (x -6)

we have that the derivative of the quotient is:

(f / g) '= (f' * g - g '* f) / g ^ 2

we replace and we have:

f (x) = [2 * x * (x-6) - 1 * x ^ 2] / (x -6) ^ 2

simplifying we have:

f (x) = [x ^ 2 - 12 * x] / (x -6) ^ 2

this must be equal to 0, like this:

 [x ^ 2 - 12 * x] / (x -6) ^ 2 = 0

we solve:

x ^ 2 - 12 * x = 0

x * (x - 12) = 0

Thus:

x = 0

x - 12 = 0 => x = 12

The critical points are 12 and 0.

B

Step-by-step explanation:

The trick you need to employ is that when the rock hits the ground, the timer stops. So h must be taken as 0.

0 = - 16t^2 + 255            Set up the equation

- 255 = - 16t^2                Divide by -16

15.9375 = t^2                  Switch

t^2 = 15.9375                   Take the square root of both sides.

sqrt(t^2) = sqrt(15.9375)

t = 3.992 seconds

The closest answer is B