Question

How do you determine the intervals for which the function is increasing or decreasing given `f(x)=(x+3)^2-4`?

Answer 1

Since the second derivative is greater than 0 (positive), -3 is a local Minimum

Explanation:

Second Derivative Test

When a function's slope is zero at x, and the second derivative at x is:

less than 0, it is a local maximum
greater than 0, it is a local minimum

`y = f(x) = (x+3)^2 - 4`

`y' = (d/dx)y = 2 * (x + 3)`

Equating to 0, we get, color(red)(x = -3)#

Second Derivative Test :

`y" = ((d^2 y)/dx^2) = 2`

Since the second derivative is greater than 0 (positive), -3 is a local Minimum