Question

Calculus Question:
If I take the derivative of a function, and plot those critical points, do I test a number from each interval into the y' function

Answer 1

you mean to find increasing/decreasing intervals?
yes

Answer 2

yes, to find inc and dec

Answer 3

yes.

Answer 4

thanks guys

Answer 5

well for your info, if you plug values into y'', you will know whether the graph trend is concave upwards or downwards. that will help you in sketching graph too.

Answer 6

thanks

Answer 7

\[
y=4 x^5-45 x^4+180 x^3-310
x^2+240 x\\
y'=
20 x^4-180 x^3+540 x^2-620
x+240=\\
y'=20 (x-4) (x-3) (x-1)^2
\]
You should not consider x=1 at all since (x-1)^2 is greater or equal to zero. To study the sign of y' in this case you study the sign of (x-4)(x-3) only.

Answer 8

http://www.wolframalpha.com/input/?i=graph+y%3D4x%5E5+%E2%88%9245x%5E4+%2B180x%5E3+%E2%88%92310x%5E2+%2B240x+

Answer 9

why would we not include x=1, it is a critical number

Answer 10

the whole purpose of sign analysis is that we can talk about the graph of the original function without actually graphing it, the days where technology did not exist

Answer 11

x=1 is a critical point. it may be a max/min point. once you plug into y'' you will know the nature of it.

Answer 12

At x=1, you cannot have a maximum or a minimum. The derivative has the same sign before 1 and after 1. So it either increasing thru 1 or decreasing thru 1.
To have a max say, f has to be increasing before 1 and decreasing after 1.

Answer 13

x=1 can be an inflection point. Actually it is.

Answer 14

yea sorry it's not a max/min point. but if i'm nt mistaken it's an inflection point.

Answer 15

yes the value of y'' changes from - to +.

Answer 16

Read the following research paper excerpt and answer the question.

According to Mario Pei, slang is common to English as well as to foreign languages (80).

Answer 17

Write the equation of the piecewise function u0192 that is represented by its graph.

Answer 18

build the wall at the border, change me mind

Answer 19

Last three

Answer 20

what tools do I need to make someone dissapear?

Answer 21

https://prnt.sc/l7sij9

Answer 22

Help on second part

Answer 23

What is the value of x ?

Answer 24

if I digest flex seal will it provide a protective layer on my organs?

Answer 25

PLS HELP!!!
https://dlap.gradpoint.com/Resz/~0.hpA-mOMelFMyUA6.E8nsNCbP7Zj4DzTvgH2qOowctLoNnspM1VAi3Bx1-jg/7234256,D47/Assets/questions/quiz/precalculus/pca

Answer 26

which expressions are equivalent to u221a25d u00b7 d 1/3 ?

Answer 27

Write the equation of the piecewise function u0192 that is represented by its graph.

Answer 28

Orgo II Mini-Tutorial: Bayer-Villiger Oxidation

Answer 29

ud835udc53(ud835udc65) = ud835udc65^2 + 1, ud835udc54(ud835udc65) = u221aud835udc65.

Answer 30

How many mL of water are required to make up a 1.87M solution if you start with 0.

Answer 31

math help plz
An experiment consists of drawing 1 card from a standardu200b 52-card deck.

Answer 32

A. The speaker describes how, even now, he lies down by his beloved in her "sepulchre there by the sea.

Answer 33

Answer check

Answer 34

Billy is trying to convince Sam that all square roots are irrational. To support his argument, Billy points out that sqrt(2), sqrt(6), sqrt(7), and sqrt(15)

Answer 35

Part A

What is the main idea of this part of the poem?

A. Annabel Lee's kinsmen took her from the speaker because she was highborn.