💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

Like

Report

DM
Numerade Educator

Like

Report

Problem 18 Medium Difficulty

The graph of a function $ f $ is shown.

(a) Find the average rate of change of $ f $ on the interval $ [20, 60] $.
(b) Identify an interval on which the average rate of change of $ f $ is 0.
(c) Which interval gives a larger average rate of change, $ [40, 60] $ or $ [40, 70] $?
(d) Compute $ \dfrac{f(40) - f(10)}{40 - 10} $; what does this value represent geometrically?

Answer

a) 10
b) Rate of change is 0 on the interval $[10,50]$
c) Rate of change is higher on the interval $[40,60]$
d) see solution

Discussion

You must be signed in to discuss.
SA

Sharieleen A.

October 26, 2020

Compliment the educator

SA

Sharieleen A.

October 26, 2020

This will help alot with my midterm

Video Transcript

this problem. Were given a function F or the graph? We're asked to find the average rate of change of F on the interval. I will do. The average rate of change is a R O C. Yeah, this is a Yeah, on Centerville 20 to 60. Well, the average rate of change formula is simply F at 60 f 20 over 60 minus 20. Right? So these are are coordinated here and here coordinated as well. And so from the graph we can see that f of 60 f of 60 is 700 and f of 20 Is 300 off of our graph. And therefore the average rate of change is 700 -300 over 60 minus 20 Which is 400 over 40, which is 10. Okay, so we got the average rate of change. That was part A. So then part B says To identify an interval in which the average rate of change of F is zero. Okay, the average rate of change is zero. So when that happens, that means that f of x two -F of X. one is 0. Or in other words our function and at one value of X has the same value as a function at another value of X. Mm. So we could pick any number of points on here. As long as our function has these two values the same. Well, we can notice that f of 10 is 400 F of 50 is also 400. So therefore We could choose this interval from 10 to 50. Right? Where the function values are the same And when that happens then the average rate of change is going to be zero because our numerator will be zero. So then part C says which interviewed gives a larger average rate of change from 40 to 60 or 40 to 70. Well, looking at the graph, Okay, the average rate of change from 40 to 60 First notice, let's read all the values off the graph. So f of 40 is 200 f of 60 is 700 And f at 70 is 900. Okay, so then the average rate of change from 40 to 60 is going to be 700 -200 over 60 minus 40. So that's 500 over 20, Which is 25. I see the average rate of change From 40 to 70, It's going to be 900 -200 Over 70 -40, Which is going to be 700 over 30 which is 70/3, which is greater which is less than 25 Because three times 25 is 75. So the average rate of change from 40 to 70 Let me just say that, say it's simply how would you rate of change from 40 to 60 is greater? Then the average rate of change from 40 to 70

DM
Oklahoma State University
Top Calculus 1 / AB Educators
Grace H.

Numerade Educator

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Michael J.

Idaho State University