(Requires Calculus) In the equation $\widehat { \text { TestScore } } = 607.3 + 3.85 \text { Income } - 0.0423 \text { Income } { } ^ { 2 }$
the following income level results in the maximum test score
A) 607.3 .
B) 91.02 .
C) 45.50 .
D) cannot be determined without a plot of the data.

Question

(Requires Calculus) In the equation $\widehat { \text { TestScore } } = 607.3 + 3.85 \text { Income } - 0.0423 \text { Income } { } ^ { 2 }$
the following income level results in the maximum test score
A)  607.3 .
B)  91.02 .
C)  45.50 .
D) cannot be determined without a plot of the data.

Quizplus · Accepted Answer

To find the income level that maximizes the test score, take the derivative of the equation with respect to Income, set it to zero, and solve for Income. The derivative is $3.85 - 0.0846 \times \text{Income}$. Setting it to zero gives $\text{Income} = \frac{3.85}{0.0846} \approx 45.50$.

(Requires Calculus) in the Equation TestScore ^=607.3+3.85 Income −0.0423 Income 2\widehat { \text { TestScore } } = 607.3 + 3.85 \text { Income } - 0.0423 \text { Income } { } ^ { 2 } TestScore =607.3+3.85 Income −0.0423 Income 2

(Requires Calculus) in the Equation $\widehat { \text { TestScore } } = 607.3 + 3.85 \text { Income } - 0.0423 \text { Income } { } ^ { 2 }$