Determine the intervals on wich f(x)=4-x^2 is increasing and the intervals on wich it is decreasing.f(x)= 4-x^2

In order to determine the intervals on which  f(x) is an
increasing or decreasing function, we'll do the first derivative
test.

If the first derivative of the function is positive,
then the function is increasing.

If the first derivative of
the function is negative, then the function is
decreasing.

We'll calculate the derivative of
f(x):

f'(x) = (4-x^2)'

f'(x) =
-2x

We'll put f'(x) = 0.

-2x =
0 for x = 0.

If x<0, then -2x >
0, so f'(x) is positive, then the function is increasing over the interval
(-infinite,0).

For x>0, then
-2x<0.

But f'(x) = -2x, so f'(x) is
negative.

If f'(x) is negative, the function
is decreasing over the interval
(0,+infinite).

For x = 0, the
function has an extreme point, namely a maximum
point.

f(0) =
4

The maximum point is:
(0,4).