×
Log in to StudySoup
Get Full Access to CU - MATH 1300 - Class Notes - Week 4
Join StudySoup for FREE
Get Full Access to CU - MATH 1300 - Class Notes - Week 4

Already have an account? Login here
×
Reset your password

CU / Math / APM 1300 / What does a negative velocity indicate?

What does a negative velocity indicate?

What does a negative velocity indicate?

Description

School: University of Colorado
Department: Math
Course: Calculus 1
Professor: Katharine adamyk
Term: Spring 2016
Tags: Calculus
Cost: 25
Name: Week 4 - Calculus 1
Description: These notes cover Week 4 of the final material before the exam.
Uploaded: 02/06/2016
2 Pages 146 Views 0 Unlocks
Reviews


ol.lst-kix_eol46ft40hzs-8.start{counter-reset:lst-ctn-kix_eol46ft40hzs-8 0}.lst-kix_eol46ft40hzs-8 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-8,lower-roman) ". "}.lst-kix_eol46ft40hzs-5 > li:before{content:"(" counter(lst-ctn-kix_eol46ft40hzs-5,lower-roman) ") "}.lst-kix_3f1merjrbz6d-3 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-3}ol.lst-kix_3f1merjrbz6d-5.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-5 0}.lst-kix_eol46ft40hzs-6 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-6,decimal) ". "}.lst-kix_eol46ft40hzs-8 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-8}.lst-kix_eol46ft40hzs-7 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-7,lower-latin) ". "}.lst-kix_eol46ft40hzs-3 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-3}.lst-kix_91e3e5vca5ek-0 > li:before{content:"- "}.lst-kix_91e3e5vca5ek-1 > li:before{content:"- "}.lst-kix_eol46ft40hzs-2 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-2}ol.lst-kix_eol46ft40hzs-5.start{counter-reset:lst-ctn-kix_eol46ft40hzs-5 0}ol.lst-kix_3f1merjrbz6d-8.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-8 0}.lst-kix_3f1merjrbz6d-0 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-0,decimal) ". "}.lst-kix_3f1merjrbz6d-2 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-2}ol.lst-kix_eol46ft40hzs-7.start{counter-reset:lst-ctn-kix_eol46ft40hzs-7 0}ol.lst-kix_3f1merjrbz6d-1.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-1 0}.lst-kix_3f1merjrbz6d-1 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-1,lower-latin) ". "}.lst-kix_3f1merjrbz6d-5 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-5}.lst-kix_3f1merjrbz6d-8 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-8}ol.lst-kix_eol46ft40hzs-4.start{counter-reset:lst-ctn-kix_eol46ft40hzs-4 0}ol.lst-kix_3f1merjrbz6d-4.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-4 0}ol.lst-kix_eol46ft40hzs-1.start{counter-reset:lst-ctn-kix_eol46ft40hzs-1 0}ol.lst-kix_3f1merjrbz6d-7.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-7 0}ol.lst-kix_3f1merjrbz6d-0.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-0 0}ol.lst-kix_eol46ft40hzs-3.start{counter-reset:lst-ctn-kix_eol46ft40hzs-3 0}.lst-kix_eol46ft40hzs-6 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-6}ol.lst-kix_eol46ft40hzs-8{list-style-type:none}.lst-kix_3f1merjrbz6d-0 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-0}.lst-kix_eol46ft40hzs-0 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-0}.lst-kix_3f1merjrbz6d-6 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-6}ol.lst-kix_eol46ft40hzs-6{list-style-type:none}ol.lst-kix_eol46ft40hzs-7{list-style-type:none}ol.lst-kix_eol46ft40hzs-4{list-style-type:none}ol.lst-kix_eol46ft40hzs-5{list-style-type:none}ul.lst-kix_91e3e5vca5ek-8{list-style-type:none}ol.lst-kix_eol46ft40hzs-2{list-style-type:none}ol.lst-kix_eol46ft40hzs-3{list-style-type:none}ol.lst-kix_eol46ft40hzs-0{list-style-type:none}ol.lst-kix_eol46ft40hzs-1{list-style-type:none}ol.lst-kix_3f1merjrbz6d-3.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-3 0}ul.lst-kix_91e3e5vca5ek-4{list-style-type:none}ul.lst-kix_91e3e5vca5ek-5{list-style-type:none}.lst-kix_3f1merjrbz6d-5 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-5,lower-roman) ". "}ul.lst-kix_91e3e5vca5ek-6{list-style-type:none}ul.lst-kix_91e3e5vca5ek-7{list-style-type:none}ol.lst-kix_eol46ft40hzs-0.start{counter-reset:lst-ctn-kix_eol46ft40hzs-0 0}.lst-kix_eol46ft40hzs-5 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-5}.lst-kix_3f1merjrbz6d-3 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-3,decimal) ". "}.lst-kix_3f1merjrbz6d-4 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-4,lower-latin) ". "}.lst-kix_3f1merjrbz6d-2 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-2,lower-roman) ". "}.lst-kix_eol46ft40hzs-7 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-7}ol.lst-kix_3f1merjrbz6d-2{list-style-type:none}.lst-kix_91e3e5vca5ek-8 > li:before{content:"- "}ol.lst-kix_3f1merjrbz6d-1{list-style-type:none}ol.lst-kix_3f1merjrbz6d-4{list-style-type:none}.lst-kix_eol46ft40hzs-4 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-4}ol.lst-kix_3f1merjrbz6d-3{list-style-type:none}.lst-kix_91e3e5vca5ek-7 > li:before{content:"- "}ol.lst-kix_eol46ft40hzs-2.start{counter-reset:lst-ctn-kix_eol46ft40hzs-2 0}ol.lst-kix_3f1merjrbz6d-0{list-style-type:none}ol.lst-kix_3f1merjrbz6d-6.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-6 0}.lst-kix_eol46ft40hzs-1 > li{counter-increment:lst-ctn-kix_eol46ft40hzs-1}ul.lst-kix_91e3e5vca5ek-0{list-style-type:none}ul.lst-kix_91e3e5vca5ek-1{list-style-type:none}ul.lst-kix_91e3e5vca5ek-2{list-style-type:none}ul.lst-kix_91e3e5vca5ek-3{list-style-type:none}ol.lst-kix_3f1merjrbz6d-6{list-style-type:none}.lst-kix_91e3e5vca5ek-2 > li:before{content:"- "}ol.lst-kix_3f1merjrbz6d-5{list-style-type:none}.lst-kix_3f1merjrbz6d-6 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-6,decimal) ". "}ol.lst-kix_3f1merjrbz6d-8{list-style-type:none}ol.lst-kix_3f1merjrbz6d-7{list-style-type:none}.lst-kix_eol46ft40hzs-1 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-1,lower-latin) ") "}.lst-kix_3f1merjrbz6d-7 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-7,lower-latin) ". "}.lst-kix_3f1merjrbz6d-8 > li:before{content:"" counter(lst-ctn-kix_3f1merjrbz6d-8,lower-roman) ". "}.lst-kix_eol46ft40hzs-0 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-0,decimal) ") "}.lst-kix_eol46ft40hzs-2 > li:before{content:"" counter(lst-ctn-kix_eol46ft40hzs-2,lower-roman) ") "}.lst-kix_3f1merjrbz6d-4 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-4}.lst-kix_3f1merjrbz6d-1 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-1}.lst-kix_91e3e5vca5ek-3 > li:before{content:"- "}.lst-kix_91e3e5vca5ek-4 > li:before{content:"- "}.lst-kix_91e3e5vca5ek-5 > li:before{content:"- "}.lst-kix_eol46ft40hzs-4 > li:before{content:"(" counter(lst-ctn-kix_eol46ft40hzs-4,lower-latin) ") "}ol.lst-kix_eol46ft40hzs-6.start{counter-reset:lst-ctn-kix_eol46ft40hzs-6 0}ol.lst-kix_3f1merjrbz6d-2.start{counter-reset:lst-ctn-kix_3f1merjrbz6d-2 0}.lst-kix_eol46ft40hzs-3 > li:before{content:"(" counter(lst-ctn-kix_eol46ft40hzs-3,decimal) ") "}.lst-kix_91e3e5vca5ek-6 > li:before{content:"- "}.lst-kix_3f1merjrbz6d-7 > li{counter-increment:lst-ctn-kix_3f1merjrbz6d-7}

Ex. Find tangent line of  2

  1. Find derivatives… 3-6a (done in problem before)
  2. Plug in unknown to find slope… 3-6(2)=-9
  3. Plug unknown into the original equation…
  4. Put point-slope in point-slope line version… y-(-6)=-9(x-2) or y=-9x+12

Y-(y value) = slope (x-xvalue)We also discuss several other topics like What are characteristics of a good theory?

                                                        Points                        DerivativeIf you want to learn more check out What are the four types of mutation?

                                                        f(0) ≈ 0                        f’(0) ≈ 0

                                                        f(1) ≈ 1                        f’(1) ≈ 2If you want to learn more check out senor plural

f(2) ≈ 4                        f’(2) ≈ 4

f(-1) ≈ 1                f’(-1) ≈ 2

                                                                                        ↗We also discuss several other topics like Why is fertility harder to measure mortality?

                                                        These values are the approximate slope of Don't forget about the age old question of Why is Africa considered as humanity's evolutionary eden?

The tangent line at that point.

If you want to learn more check out What are lipid bilayers?

Velocity

 means the velocity at time x

⤷ A negative velocity indicates a backward direction

Derivative Function

 or

        When slope of original is unchanging,

        the derivative has horizontal lines on

        that interval.

                                                        Notations        original = f(x) / position

                                                        First derivative = / // velocity

                                                        Second derivative = / acceleration

                                                        Third Derivative = / jerk

Differentiability

Differentiable → able to take derivative

Non-differentiable → unable to take derivative

  1. Non-continuous functions - hole, asymptote, jump
  2. Vertical tangent line
  3. Corner (or cvsp)

⛤ If original is dis-continuous, derivative must be discontinuous ⛤

⛤ But original can be continuous while derivative is still discontinuous⛤

                differentiable ⇒ continuous

Relationship between

Original

Derivative

Increasing at a

Above x axis (positive)

Decreasing at a

Below x axis (negative)

Horizontal tangent line

X-intercept (0)

Cusp / discontinuous / vertical line

undefined

Positive slope line crosses x axis

Negative slope line crosses x axis

linear

Horizontal line

Page Expired
5off
It looks like your free minutes have expired! Lucky for you we have all the content you need, just sign up here