Question

The function f ( x ) is graphed below. In two or more complete sentences, describe how to find the interval(s) where the function is decreasing and how interval notation is used to express the interval(s). In your final answer, include the interval in which the function is decreasing.

Answer 1

f(x) is strictly monotonically decreasing in [-5 , 0]

Explanation:

The function f(x) will be

I )monotonically decreasing in an intervel (a ,b)

iff f'(x) ≤ 0 ∀ x ∈ ( a , b) [ when f(x) is derivable in (a,b)]

II) strictly monotonically decreasing in an intervel (a ,b)

iff f'(x) < 0 ∀ x ∈ ( a , b) [ when f(x) is derivable in (a,b)]

Here, although f(x) is not specified, but from the graph it is evident that f(x) is strictly monotonically decreasing in [-5 , 0]

1. x ∈ (a , b) means a < x <b

2. x ∈ [a, b) means a ≤ x < b

3. x ∈ (a , b] means a < x ≤ b

4. x ∈ [a , b] means a ≤ x ≤b

This is how interval notations are used.