the table describes rates of change of a function $f$ for selected intervals of $x$. the function $f$ is defined for $0leq xleq4$. on which of the following intervals is the graph of $f$ concave down?

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Accepted Answer

# Explanation:
## Step1: Recall concavity - rate - of - change relationship
The graph of a function $y = f(x)$ is concave down when the rate of change of the function (its derivative $f^\prime(x)$) is decreasing.
## Step2: Analyze the intervals
In the interval $0<x<1$, the rate of change of $f$ is increasing, so the function is concave up. In the interval $1 < x<2$, the rate of change is positive and constant, so the function is linear (neither concave up nor down). In the interval $2<x<3$, the rate of change of $f$ is decreasing. In the interval $3<x<4$, the rate of change is negative and constant, so the function is linear.

# Answer:
$2 < x<3$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall concavity - rate - of - change relationship

Step2: Analyze the intervals

Answer: