im having trouble finding the intervals of increase and decrease.
i got the derivative to be (x^3+4)/(x^3-8)^2 and proceeded to find the critical numbers.
my critical numbers were: (-4)^(1/3) and 2
i plugged the numbers into the derivative to check where f'(x) was positive and negative to see where f(x) is increasing and decreasing.
the sign graph showed that f(x) is decreasing from -infintity to (-4)^(1/3) and increasing from (-4)^(1/3) to infinity.
this is where i feel like i went wrong somewhere.because when i found the second derivative and the concavity, its concave down from -infinity to 2. so shouldnt f'(x) be positive from -infinity to (-4)^(1/3) and negative to the right of that?
and plus i cheated and looked at the function a graphing calculator and the f(x) is not decreasing from the left of (-4)^(1/3) and then increasing.
i got the derivative to be (x^3+4)/(x^3-8)^2 and proceeded to find the critical numbers.
my critical numbers were: (-4)^(1/3) and 2
i plugged the numbers into the derivative to check where f'(x) was positive and negative to see where f(x) is increasing and decreasing.
the sign graph showed that f(x) is decreasing from -infintity to (-4)^(1/3) and increasing from (-4)^(1/3) to infinity.
this is where i feel like i went wrong somewhere.because when i found the second derivative and the concavity, its concave down from -infinity to 2. so shouldnt f'(x) be positive from -infinity to (-4)^(1/3) and negative to the right of that?
and plus i cheated and looked at the function a graphing calculator and the f(x) is not decreasing from the left of (-4)^(1/3) and then increasing.