Question

find the intervals on which f is increasing
\[4-x ^{2}\]

Answer 1

Solve for where the solution is positive and negative. Positive = increasing, negative = decreasing.

Answer 2

and how do i do that

Answer 3

At this moment, I would say plug in numbers. i.e. \[4-(3)^2\] =4-9= -5
So negative and decreasing.

Answer 4

You can assumed any number larger than 3 will also be negative.

Answer 5

Essentially, x^2 larger than 4 will be negative but x^2 less than 4 is positive.

Answer 6

ummm no that's definitely not how it has something to do with finding the derivative but idk where to go from there

Answer 7

Oh! I didn't understand where you were at in your math class. In that case:

Answer 8

yes?

Answer 9

So set your derivative equal to 0.

Answer 10

That gives you a critical number, the term you will base your intervals around.

Answer 11

Different people go about the next step in different ways, but basically you want to find where the derivative is positive or negative.

Answer 12

I suggest a number line: