Supposef(0) = 2 and 2 ≤ f '(x) ≤ 7for all x in the interval [−5, 5]. determine the greatest and least possible values of f(2).least

If the slope of the function is 2, the amount it can change over the interval 0–2 is

... 2×2 = 4 units

If the slope is 7, the amount it can change over the interval 0–2 is

... 2×7 = 14 units

The least possible value of f(2) is 2+4 = 6.

The greatest possible value of f(2) is 2+14 = 16.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

where is the picture

step-by-step explanation: