Question

the following is the graph of a function (y = f(x)). where is the graph decreasing and concave up? (select all that apply.)

Explanation:

Step1: Recall function properties

A function is decreasing when its first - derivative \(f'(x)<0\) and concave up when its second - derivative \(f''(x)>0\). Visually, a decreasing function has a negative slope and a concave - up function curves upwards like a cup.

Step2: Analyze the graph

By observing the given graph of \(y = f(x)\), we look for intervals where the curve is going downwards (decreasing) and curving upwards (concave up).

Step3: Identify intervals

In the given intervals:

• For \(0 < x<0.5\), the function is decreasing and concave up.
• For \(1.5 < x<2\), the function is decreasing and concave up.
• For \(3 < x<3.5\), the function is decreasing and concave up.

Answer:

0 < x<0.5, 1.5 < x<2, 3 < x<3.5