#Must be positive?

66 messages · Page 1 of 1 (latest)

proven rock
#

About the problem at 5:13 on https://www.khanacademy.org/math/ap-calculus-ab/ab-integration-new/ab-6-5/v/interpreting-behavior-of-antiderivative , notice the tab transcript, and screenshot attached. I have a hard time understanding. I thought integral were about change and not quantity. Does the problem mean a positive change or positive value, of whatever quantity is changing? If the latter, I fail to understand the host explanation about how the quantity must be positive.

Although if negative quantity is possible, I'm assuming it's one that can be, eg temperature.

tmp185.png
livid dewBOT
#
  1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
  2. Wait patiently for a helper to come along.
  3. Once someone helps you, say thank you and close the thread with:
    +close
  4. Feel free to nominate the person for helper of the week in #helper-nominations
  5. Do not ping the mods, unless someone is breaking the rules. If there is a conflict amongst multiple helpers feel free to ping “Helper Mod”
  6. If you're happy with the help you got here, and the server overall, you can contribute financially as well:
heady spear
proven rock
#

I don't understand.

heady spear
#

We have it's derivative f'(x).

#

(If you want to learn it on your own, go back to Unit 5 Lessons 3-8)

proven rock
#

I doubt the host call it antiderivative though,.

heady spear
gritty vapor
heady spear
#

stupid me

gritty vapor
proven rock
#

yes, originating from Riemann IIRC

heady spear
heady spear
proven rock
#

I'll keep it in mind, would you kindly answer the OP questions?

heady spear
#

Here, we are trying to prove g is positive

#

on [7,12]

#

now for this i will give an example graph

#

black line is y=2x, red one is y=2

#

red is the derivative of black

#

do you see how 2x>0 when x>0?

proven rock
#

yes

heady spear
#

uh oh

#

i gotta eat

#

give me ~15-20 mins

#

and ill be back

proven rock
#

k

heady spear
#

just try to analyze and create other graphs

proven rock
#

if I don't type, pleasse continue to explain

heady spear
#

graph x^2 and 2x

#

and notice how 2x is increasing for all x

proven rock
#

Is this what the OP image result in?

tmp186.png
#

notice there's 2 straight lines

#

and if so, can'T it just be shifted down so a part (or whole) be negative?

#

as in the OP suggest it could simply be temperatures

heady spear
proven rock
#

I did not draw a derivative, the original value, the base unit

#

the temperature, distance, etc

heady spear
proven rock
#

why can't the curve be shifted down?

#

why can't there be ice in the pot on the stove?

#

@heady spear☝️

heady spear
#

derivative of g(x) (which is f(x)) is constant and non-negative on teh interval

#

when derivative is constant it means function increasing

#

you could technically shift the curve down

#

but we are looking at g'(x)=f(x)

proven rock
#

oh... on the stove would always be an increase even if the base is negative at the start.

#

the opposite with boiling water in a freezer

heady spear
#

sorry i was working

proven rock
#

did you not think of explaining it like that, or were you forcing me to?

heady spear
#

was too busy to explain

#

also its good for you to figure it out on your own

#

me telling you a concept doesn't help

#

you teaching youself helps more

urban jettyBOT
#

@proven rock

<:HelpIcon:1304095958283321385>| Help Reminder

Hello dynv_, this is a friendly reminder that your thread has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command.

unborn drift
#

+close