The graph below models the height of a remote-control helicopter over 20 seconds during flight. Time (seconds)
Over which interval does the helicopter have the slowest average rate of change?
1) O to 5 seconds
3) 10 to 15 seconds
2) 5 to 10 seconds
4) 15 to 20 seconds

2) 5 to 10

Step-by-step explanation:

The slowest average rate change will occur when, as time progresses, the height of the helicopter changes very little.

Analyzing the intervals:

In the interval from 0 to 5, the height of the helicopter, according to the graph, changes drastically.

In the interval from 5 to 10 the height hardly changes.

In the interval from 10 to 15 the height changes more than in the previous interval (downward).

And in the interval from 15 to 10 something similar the the previous interval happens, but upwards.

thus, the interval that has the smallest average rate of change is 5 to 10 since there is not much change in the height over this interval of time (compared to the other intervals).

answear:

a

step-by-step explanation: a

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.