Question

Question #7c46f

Answer 1

the second and fourth choices.

Explanation:

I think you should graph this if you are learning pre-calculus right now.
When we graph the function `f(x)=(x+2)^3`, we get:
graph{(x+2)^3 [-10, 10, -5, 5]}

You can see that the curve goes up constantly, except around `x=-2`. Hmm. We need a bit better tactic.

You could also use derivatives for this problem.

First, we find the derivative of `(x+2)^3` using the power rule and the chain rule.
`f(x)=(x+2)^3` =>`f'(x)=3(x+2)^2xx1`
Now, remember that a function is increasing when its derivative is greater than zero.

Therefore, we have the inequality:
`0<3(x+2)^2xx1` simplify this to get:
`0<(x+2)^2`
We see that no real number plugged into the inequality can give us a negative value. However, we see that it gives the answer of zero when `x=-2`. Therefore, the function is increasing when `x> -2` and `x<-2`. graph{3(x+2)^2 [-10, 10, -5, 5]}
This graph shows what the instantaneous rate of change is for a give value of x. It is positive for any x values except at `x=-2` ; the instantaneous rate of change there is 0.

If you were taught to do this by graphing, this problem was probably intended for you to use logic to eliminate the wrong choices.