Question

the graph of the derivative f(x) of a continuous function f is shown. on what intervals is f decreasing? (description: a function in two disjoint continuous parts is graphed on the xy coordinate plane. the first part of the function is a curve that starts at an open circle at approximately (3,2), goes down and to the right, crosses the x - axis at approximately (4,0), reaches a low point, goes up and to the right, crosses the x - axis at approximately (6,0), and terminates at an open circle at approximately (7,2). the second part of the function starts at an open circle at approximately (7, negative 4), goes up and to the right, crosses the x - axis at approximately (9,0), and exits the top right of the viewing window.) (8,9) (4,6)∪(7,9) (2,6) (-1,1) none of these

Explanation:

Step1: Recall the relationship between a function and its derivative

A function $f(x)$ is decreasing when $f'(x)<0$.

Step2: Analyze the graph of $f'(x)$

From the description of the graph of $f'(x)$, we see that $f'(x)<0$ on the intervals $(4,6)$ and $(7,9)$.

Answer:

$(4,6)\cup(7,9)$