# Thread: Find the intervals INC/DEC

1. ## Find the intervals INC/DEC

For the function f(x) find the intervals on which it is inc/dec.

f(x)= x⁴ - 4x³ + 10
f'(x) = 4x³ - 12x² or 4x²(x - 3) => x=3

so i have the intervals (-∞, 3) and (3, ∞) i'm using the test values 1 and 4 and im plugging my test values into f'(x).

I'm getting -8 for the test value 1 so its decreasing, and 64 for the test value 4 so it's increasing.

DEC on (-∞, 3) and INC on (3, ∞).

My professor got INC on (-∞ , 3) ; DEC on (3, ∞) can you spot what i'm doing wrong?

2. Originally Posted by Johnny Walker Black For the function f(x) find the intervals on which it is inc/dec.

f(x)= x⁴ - 4x³ + 10
f'(x) = 4x³ - 12x² or 4x²(x - 3) => x=3

so i have the intervals (-∞, 3) and (3, ∞) i'm using the test values 1 and 4 and im plugging my test values into f'(x).

I'm getting -8 for the test value 1 so its decreasing, and 64 for the test value 4 so it's increasing.

DEC on (-∞, 3) and INC on (3, ∞).

My professor got INC on (-∞ , 3) ; DEC on (3, ∞) can you spot what i'm doing wrong?
I do not agree w/ your professor.

$\displaystyle f'(x) = 4x^2(x-3) = 0$

critical values of $\displaystyle x$ are $\displaystyle x = 0$ and $\displaystyle x = 3$

the factor $\displaystyle 4x^2 > 0$ for all $\displaystyle x \ne 0$

$\displaystyle x-3 < 0$ for all $\displaystyle x < 3$ ... $\displaystyle f(x)$ is decreasing

$\displaystyle x-3 > 0$ for all $\displaystyle x > 3$ ... $\displaystyle f(x)$ is increasing

graph attached.

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