Question

Determine the open intervals on which the function is increasing

and on which the function is decreasing. Enter ∅ to indicate the
interval is empty. f(x)=2x2−8x+7

Answer 1

The function is increasing on the interval (2, ∞) and decreasing on the interval (-∞, 2).

Step-by-step explanation:

To determine the intervals on which a function is increasing or decreasing, we need to find the intervals where the derivative of the function is positive or negative.

The derivative of the function f(x) = 2x^2 - 8x + 7 is f'(x) = 4x - 8.

To find the intervals of increase or decrease, we need to solve f'(x) > 0 and f'(x) < 0.

Solving f'(x) > 0, we get x > 2. Solving f'(x) < 0, we get x < 2.

Therefore, the function is increasing on the interval (2, ∞) and decreasing on the interval (-∞, 2).