MartynaJ
Homework Statement:
Sketch a possible graph for the function that satisfies all of the following criteria and justify
your sketch by clearly labelling each of the given information.
□ Average rate of change = 5 for t belongs to [1, 5]
□ Average rate of change = -20 for t belongs to [1,10]
□ Average rate of change = 0 for t belongs to [2 , 9]
□ Instantaneous rate of change = -10 at t = 2
□ Instantaneous rate of change = 0 at t =3
Relevant Equations:
So I attempted this problem and to satisfy the first condition (for t in the range of [1, 5]), I drew the straight line that has a slope of 5 (i.e. f(x)=5x). I just don't understand how I can have the same function with a different slope (average rate of change) for the interval [1,10] or for [2 , 9]... Any help please!

Gold Member
As for the first statement it means, say f(t)
$$f(5)-f(1)=5(5-1)=20$$ and so on.

• WWGD, Delta2 and DaveE
Gold Member
By "average rate of change" they mean the average slope over the specified interval. So, for example, you can have an average slope of 5 over [1, 5] with a line that is flat on [1, 3.5] and has a slope of 10 on [3.5, 5].

Frankly I'm not sure what "instantaneous rate of change" means. I would guess it means "constant rate of change" or "rate of change at each point".

Homework Helper
Gold Member
2022 Award
you can have an average slope of 5 over [1, 5] with a line that is flat on [1, 3.5] and has a slope of 10 on [3.5, 5].
Wouldn't that give an overall change of 15 instead of 20?
what "instantaneous rate of change" means
It just means the slope at that point.