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Calculus 151 Regression Project. Data collected from the NJ Department of Education Website. NJ Standardized Test Scores. 76.8 – 75.2 1.6 Average Rate of Change = 02 - 11 = -9 = - .778. Sine Regression. Instantaneous Rate of Change at 2003 = -5.174.

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Calculus 151 regression project

Calculus 151 Regression Project

Data collected from the NJ Department of Education Website


Nj standardized test scores
NJ Standardized Test Scores

76.8 – 75.2 1.6

Average Rate of Change = 02 - 11 = -9 = - .778


Sine regression
Sine Regression

Instantaneous Rate of Change at 2003 = -5.174


Quartic regression r 2 555
Quartic RegressionR2 =.555

Instantaneous Rate of Change at 2003 = -1.826


Split regressions
Split Regressions

Limit x 6.5- 75.25657 Limit x 6.5+ 71.669602


Continuous split regressions
Continuous Split Regressions

Limit x 6.5 73.463086

Limit x - ∞ ∞ Limit x ∞ DNE



Derivatives of exponential logarithmic and sine regressions
Derivatives of exponential, logarithmic, and sine regressions

Y’= 74.56303051 *.9993957215^x *ln(.9993957215)

Y’= -.6345494264

x

Y’=-6.784189065* cos(-2.304469566 x + 1.333706904)


Newton s method finding zeros of the cubic regression
Newton’s Methodfinding zeros of the cubic regression

X0=23.74251964

X0=23.74251964


Mean value theorem
Mean Value Theorem

f’(c) = 75.682- 76.565

11-2

f’(c) = - .883

9

f’(c) = -.098

c = X

f(c) = Y4

f’(c) = Y5

Y= -.098(x – 3.4931) + 71.661

Y= -.098(x – 6.9124) + 75.325

Y= -.098(x – 9.67854) +72.782



Max and min of cubic regression
Max and Min of Cubic Regression

The Regression has a minimum at 5.4093854 and a maximum at 10.033224. It is increasing between [5.4093854, 10.033224] ,and is decreasing between (- ∞ , 5.4093854) U (10.033224, ∞).


Second derivative of cubic regression
Second derivative of cubic regression

Second Derivative Zero

Inflection Point

Concave up

Concave down

First Derivative Maximum


Approximating area under a curve using left endpoints
Approximating area under a curve using left endpoints

Estimate Area is

668.504

72.432

73.684

77.426

74.644

76.352

71.138

76.517

74.42

71.891


Approximating area under a curve using right endpoints
Approximating area under a curve using right endpoints

Estimate Area is

670.836

76.352

71.138

76.517

74.42

71.891

77.426

72.432

73.684

76.976


Finding area under the curve using the fundamental theorem of calculus
Finding Area under the curve using the Fundamental Theorem of Calculus

11

Area=∫02 2.943926518sin(-2.304469566x+1.333706904) +74.26459702dx

F(x)= 1.277485527cos(-2.304469566x +1.333706904)+74.26459702x

F(11)- F(02)≈ 817.47-147.26≈ 670.21

Area ≈ 670.21



Average value
Average Value of Calculus

Area= the sum of the % of students proficient in Mathematics over the past 9 years

Average % of students 670.69193

proficient in Mathematics = 9 ≈ 74.55%

for each year


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