Question

Find the open intervals on which the function

f(x)=−11x²+10x is increasing or decreasing.
a)(−[infinity],5/11)is increasing,(5/11,[infinity]) is decreasing
b)(−[infinity],5/11)is decreasing,(5/11,[infinity]) is increasing
c)(−[infinity],10/11)is increasing,(10/11,[infinity]) is decreasing
d)(−[infinity],10/11) is decreasing,(10/11,[infinity]) is increasing

Answer 1

The function f(x) = -11x² + 10x is increasing on the interval (-∞, 5/11) and decreasing on the interval (5/11, ∞).

Step-by-step explanation:

To determine the intervals on which the function f(x) = -11x² + 10x is increasing or decreasing, we need to find the critical points. The critical points occur when the derivative of the function is equal to zero or undefined.

First, let's find the derivative of f(x): f'(x) = -22x + 10.

Setting f'(x) = 0 and solving for x, we get x = 5/11. We now have one critical point.

To determine the intervals of increase and decrease, we can use the first derivative test.

If f'(x) > 0, then the function is increasing. If f'(x) < 0, then the function is decreasing.

Since f'(x) = -22x + 10, we can evaluate f'(x) at a value less than 5/11 (e.g., 0) to determine if the function is increasing or decreasing.

So, the function is increasing on the interval (-∞, 5/11) and decreasing on the interval (5/11, ∞).