The graph of $f(x)=x^3-6x^2+5$ changes concavity only at $x=2$. Describe its concavity on $(-\infty ,2)$.

For $g(x)=(x-1{)}^3+4$, describe the graph on $(-\infty ,1)$.

For $q(x)=-(x+2{)}^3+1$, what is the concavity on $(-\infty ,-2)$?

Describe the graph of $r(x)=2(x-4{)}^3-7$ on $(4,\infty )$.

On $(5,\infty )$, how does the graph of $s(x)=-3(x-5{)}^3+2$ bend?

Find the point of inflection of $h(x)=(x+3{)}^3-5$.

What is the point of inflection of $a(x)=(x-4{)}^3+2$?

Locate the point of inflection for $b(x)=-2(x+1{)}^3+6$.

The function is $c(x)=5(x-2{)}^3-9$. Where is its point of inflection?

Over four consecutive equal-width intervals, a function's average rates of change are $2$, $5$, $9$, and $14$. Which description is consistent with the data?

A function has average rates of change $-3$, $-1$, $2$, and $6$ over equal-width consecutive intervals. What description is consistent?

Across four equal-width intervals, the average rates of change are $12$, $8$, $5$, and $3$. What behavior is consistent with these values?

For equal-width intervals, a function's average rates of change are $7$, $4$, $0$, and $-5$. Choose the description consistent with the data.

A town's population rises each year, but the number of new residents added each year gets smaller. Describe population versus time.

A reservoir's water level falls each day, but the amount it falls each day becomes smaller. How is water level versus time described?

A cyclist's total distance from home increases each minute, and each minute the cyclist travels farther than in the previous minute. Describe distance versus time.

A substance cools over time, and its temperature drops by a larger amount during each successive minute. Describe temperature versus time.

A smooth graph is concave down on $(-\infty ,2)$ and concave up on $(2,\infty )$, with $p(2)=3$. Is $(2,3)$ a point of inflection?

The graph of $m$ is concave up on $(-\infty ,-1)$ and concave up on $(-1,\infty )$, and $m(-1)=4$. Is $(-1,4)$ a point of inflection?

A smooth curve is concave up on $(-\infty ,5)$ and concave down on $(5,\infty )$, with $n(5)=-2$. Which statement about $(5,-2)$ is correct?