   Chapter 10.6, Problem 52E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

SAT Scores by Income The following graph shown U.S. math SAT scores as a function of parents’ income level.81 Income (\$1,000).The regression curve shown is given by f ( x ) = − 0.0034 x 2 + 1.2 x + 444    ( 10 ≤ x ≤ 180 ) where f ( x ) is the average math SAT score of a student whose parents earn x thousand dollars per year. Compute and interpret f ′ ( 30 ) .

To determine

To calculate: The value of f(30)

for the function f(x)=0.0034x2+1.2x+444, where f(x)

represents the average math SAT score of a student whose parents earn x thousand dollars per year, also interpret the answer and the graph which shows the U.S. math SAT scores as a function of parents income level is as follows: Explanation

Given information:

The function f(x)=0.0034x2+1.2x+444, where f(x)

represents the average math SAT score of a student whose parents earn x thousand dollars per year.

The graph which shows the U.S. math SAT scores as a function of parents income level is as follows:

Formula used:

The difference quotient formula is used which is as follows:

f(x)=limh0f(x+h)f(x)h

The square of the sum formula,

(a+b)2=a2+b2+2ab

Calculation:

Consider the function f(x)=0.0034x2+1.2x+444, where f(x)

represents the average math SAT score of a student whose parents earn x thousand dollars per year.

The difference quotient formula used to estimate the exact value of derivative algebraically is:

f(a)=limh0f(a+h)f(a)h

Substitute a=30

into the above formula,

f(30)=limh0f(30+h)f(30)h

Substitute the values of f(30)

and f(30+h)

in f(x),

f(30)=limh0[0.0034(30+h)2+1

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