State (in interval notation) all intervals in which the function is increasing and all intervals in which the function is decreasing. Make sure you label each interval clearly.

Question

Use desmos.com to graph the function

f (x) = x^3− 2x^2− 3x + 4.

Answer 1

Hi Melissa,

When you enter the equation into Desmos, you'll see that it increases until x = -0.535, then decreases until x = 1.869, and then increases again.

To write this in interval notation

Increasing: ( -∞ , -0.535 ) ∪ ( 1.869 , ∞ )

Decreasing: ( -0.535 , 1.869 )

__________

Another way to figure this out would be to take the derivative.

When f'(x) > 0, f(x) is increasing.

When f'(x) < 0, f(x) is decreasing.

f'(x) = 3x² - 4x - 3

When you plot this equation, you will see that the derivative is above 0 until -0.535 (increasing), below 0 until 1.869 (decreasing), and above 0 again.

We would get the same answers as above!