Graphs of change

On the graph of Keza's trip (segments A–E in the lesson), during which segment was she riding fastest?

A village water tank holds $1200$ litres at 8 a.m. and $300$ litres at 11 a.m. What is the average rate of change of the amount of water, in litres per hour?

A bamboo shoot in a garden in Kyoto is $40$ cm tall on day $0$, $130$ cm on day $3$ and $180$ cm on day $5$. What is its average rate of growth from day $0$ to day $5$, in cm per day?

A cyclist rides slowly up a steep hill, then quickly down the other side, each at a steady speed. Which describes the graph of distance travelled against time?

Over the same week, the graph of plant P's height is steeper than the graph of plant Q's height. Which statement must be true?

A bus travels $90$ km at $45$ km/h and then returns the same $90$ km at $90$ km/h. What is its average speed for the whole round trip, in km/h?

Amira cycles for a while at an average of $12$ km/h, then for a while at an average of $20$ km/h (she spends some time on each leg). Which of these could be her average speed for the whole ride? (Choose all that apply.)

Which Lean statement says that f : Rat → Rat is increasing (y gets larger whenever x gets larger)?

Write average_rates(points) for a list of points (x, y) with increasing $x$-values. Return the list of average rates of change between consecutive points, as Fractions. For Keza's journey [(0, 0), (20, 4), (25, 4), (35, 6), (55, 6), (75, 0)] (minutes, km) it should return the rates in km per minute.

In the model $d(t) = 4.9t^2$, the average speed of the falling stone over the interval from $t = 3$ to $t = 3 + h$ (with $h \neq 0$) is …