APFIVE Ordering Function and Average Values
The function $$A$$ is defined by $$A(x)=x^2+1$$. The table below provides the values of $$A(x)$$ at $$x=0, x=1$$, and $$x=2$$, along with the average value of $$A$$ on the interval $$[0,2]$$. Which of the following lists these four quantities in increasing order?
| Description | Value |
|---|---|
| Value at $$x=0$$ | 1 |
| Value at $$x=1$$ | 2 |
| Value at $$x=2$$ | 5 |
| Average value on $$[0,2]$$ | $$\frac{7}{3}\approx2.33$$ |
A
$$A(2)$$, $$A(1)$$, Average, $$A(0)$$
B
$$A(0)$$, Average, $$A(1)$$, $$A(2)$$
C
$$A(0)$$, $$A(1)$$, Average, $$A(2)$$
D
Average, $$A(0)$$, $$A(1)$$, $$A(2)$$
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