Plot Dataandgraph the Regressions. Label Axis
1. Roughlyplot dataandregression. Label Axis.
Find the averagerateof change between the first and last x-values usingregression
2. Roughlysplit the graph into two regions and performdifferentregressions on eachside.Plot dataandregressions. Label Axis.
3.Roughlysplit the graph into two regions and performdifferentregressions on eachside.Plot dataandregressions. Label Axis.
leftregression split at aY1=vars 5: >1: RegEq /(x≤a)rightregression
Y2=vars 5: >1: RegEq /(x≥a) / LeftRegressionused:
RightRegressionused:
Find Y1(-9999)
Y2(9999) / limr(x)
x
limr(x)
x
4.For acontinuousregression: Given ɛ =small number Find δ0 that satisfiesRoughlyadjust the regressions so the graph is continuous.
Plot dataandgraph the regressions. Label Axis.
BONUS
Y1(x)=regression(y2=splitregression)Y3=L- ɛY4=L+ ɛ
Calc5:intersect y1andy3 =x1Calc5:intersect y1(2)andy4 =x2δ =maximum(|a-x1|,|a- x2|) / limr(x)=L
xa
Givenɛ =
Find δ =
Pick xvalues in order
Find the averagerateof change between the exterior x-values around x =ausingregression
{Y1(x1)-Y1(x6)}/{x1–x6}= msec / AverageRate ofChangeFind the averagerateof change between an interior x-values around x=ausingregression
{Y1(x2)-Y1(x5)}/{x2–x5}= msec / AverageRate ofChangeFind the averagerateof change between themoreinterior x-values around x=ausingregression
{Y1(x3)-Y1(x4)}/{x3–x4}= msec / AverageRate ofChangeFind theinstnataneousrate of changeat x=a
nderiv(y1,x,a)or calc 6:dydx and x =a / InstantRate ofChange
6. Find the derivativesofdifferentregressions using rules at x=x1
LinearRegressiony1=ax+b / y’=a / y’(x1) =Quadratic Regressiony2=ax2+bx+c / y’=2ax+b / y’(x1) =
Cubic Regressiony3=ax3+bx2+cx+d / y’=3ax2+2bx+c / y’(x1) =
QuarticRegressiony4=ax4+bx3+cx2+dx+e / y’=4ax3+3bx2+2cx+d / y’(x1) =
Choosearegression,evaluateitatx1: y(x1)=
Accordingtothe
weexpectytobey(x1)= ofy'(x1)=
regression,atx1=
withagrowthrate
Exponentialy6=a*b^x / y’=a*b^x*ln(b) / y’(x1) =LnRegressiony7=alnx+b / y’=a/x / y’(x1) =
Choosearegression,evaluateitatx1: y(x1)=
Accordingtothe
weexpectytobey(x1)= ofy'(x1)=
regression,atx1=
withagrowthrate
8.Find thesecondderivativesofdifferentregressionsusingrulesatx=x1
LinearRegressiony1=ax+b / y’’= 0 / y’’(x1) =Quadratic Regressiony2=ax2+bx+c / y’’= 2a / y’’(x1) =
Cubic Regressiony3=ax3+bx2+cx+d / y’’= 6ax+2b / y’’(x1) =
QuarticRegressiony4=ax4+bx3+cx2+dx+e / y’’=12ax2+6bx+2c / y’’(x1) =
Choosearegression,evaluateitatx1: y(x1)=
Accordingtothe
weexpectytobey(x1)=
regression,atx1=
withagrowthrate
ofy'(x1)=
anditis
9.Makea transformation ofyour x-valuesandyoury-values
New x-values (units) / Old x-values(units)Old x-values(units) / Oldy-values(units)
Oldy-values(units) / Newy-values(units)
10.Find the derivativesof sine regression usingrulesat x=x1
Sine Regressiony2=asin(bx+c)+d / y’=acos(bx+c)*b / y’(x1) =Find the second derivatives of sine regression usingrulesat x=x1
Sine Regressiony2=asin(bx+c)+d / y’’= -asin(bx+c)*b^2 / y’’(x1) =Accordingtothesine regressionwithaperiodof
,at
x1=weexpectytobey(x1)=
withagrowthrateof
y'(x1)=
anditis
11.Usethe mean value theorem on thetwo end points OFaregressionand identifyapoint on thegraphwith a similarslope?12. Was the zerofoundbyusingNewton’s Method for byusingx=0 or x=1 as an initialguess?Y1=cubicregression
0 sto x
x-y1/nderv(y1,x,x)stox
iterationiterationiteration
zero:
13.
X:
Y’
Increasingor Deceasing
Y’’
Concavity?Up or Down
15.
Findy=0to identifycritical valuesa1,a2
Findy’’(a1)andy”(a2) todetermine max/min
Y’’atcriticalPointsMaxor Min
16. Findy’’=0 to identifyinflection points Did the student takethesecond derivative and identifyconcavityforthe zero ofthecubicregression? Y’’=0 at –b/(6a):