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

Get the answer to your homework problem.

Try Numerade Free for 7 Days

Like

Report

Coffee is being poured into the mug shown in the figure at a constant rate (measured in volume per unit time). Sketch a rough graph of the depth of the coffee in the mug as a function of time. Account for the shape of the graph in terms of concavity. What is the significance of the inflection point?

Point $A$ is an inflection point and is significant because the rate of increase in depth changes from increasing to decreasing (depth still increasing but at a slowing rate).

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 3

How Derivatives Affect the Shape of a Graph

Derivatives

Differentiation

Volume

Oregon State University

University of Nottingham

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:58

Water is pumped into a sph…

01:33

Suppose that water is flow…

02:31

01:05

01:02

02:02

Suppose a hot cup of coffe…

01:43

During a flood, the water …

01:51

In this section, we examin…

05:03

Interpreting the derivativ…

So coffee is being poured into the moat shown in the figure. So the figure is right here and what we're being asked immeasurable, impertinent time. And we're being asked to sketch a graph. Ah, rough graph of the depth of the coffee in the mug at the function of time and account for the shape of the graph in terms of Khan. Captain. So what is the significance of this inflection point? So this is a kind of a rough sketch of the pitch to coffee that's in a textbook, but you can see that it is very wide at the bottom and then gets narrow and then gets right to get so they're just kind of a general idea of what graph looks like. So this is going to be the exact that's going to depth. So they get sick, and then the Y axis will mean the Y axis will be dead in the exact it will be time. So when we first begin point coffee at a constant rate, the debt won't The death won't be ah, increasing. It's much quicker this wide, and this takes it takes more coffee to fill up so's less of being achieved, and then it's going to sort of increase as they get into the more narrow range. It gets more into the narrow aged increases really fast, and then it gets wide again and sort of does the opposite, and that is what happened to forget. And so we have an inflection points. But this is Kong cave up, and then we have can't keep down the inflection point somewhere in the middle. And so the significance of the inflection point is that at this point, the coffee eyes being poured faster at any other point. So it is being filled up. The the height or the depth of the coffee in the monk is increasing at a faster rate than any other point in the coffee mug. And that's really the important. That's really the interpretation for the inflection point. And that's really what widen what's really need about inflection. Point of telling us about the fastest rate at which it is, um, tells us a lot about different situation in this term tells us that there rated the coffees. The depth of the company is increasing at a factory than any other point

Numerade Educator

In mathematics, integration is one of the two main operations in calculus, w…

In grammar, determiners are a class of words that are used in front of nouns…

Water is pumped into a sphere at a constant rate (Figure 18 ). Let $h(t)$ be…

Suppose that water is flowing at a constant rate into the container shown. M…

Water is pumped into a sphere of radius $R$ at a variable rate in such a way…

Suppose a hot cup of coffee is left in a room for 2 hours. Sketch a reasonab…

During a flood, the water level in a river first rose faster and faster, the…

In this section, we examined supply and demand functions for coffee. Does it…

Interpreting the derivative The graph of $f^{\prime}$ on the interval [-3,2]…