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

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Answer 1 · 2018-01-26T09:27:21

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

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