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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Psychology Early in the twentieth century, an intelligence test called the Stanford-Binet Test (more commonly known as the IQ test) was developed. In this test, an individual’s mental age M is divided by the individual’s chronological age C and the quotient is multiplied by 100. The result is the individual’s IQ.

I Q ( M , C ) = M C × 100

Find the partial derivatives of IQ with respect to M and with respect to C. Evaluate the partial derivatives at the point (12, 10) and interpret the result. (Source: Adapted from Bernstein/Clark-Stewart/Roy/Wickens, Psychology, Fourth Edition)

To determine

To calculate: The value of the partial derivative of IQ with respect to M and with respect to C, also calculate the value of the partial derivative at the point (12,10) and interpret the result if the function for IQ level is modelled by IQ(M,C)=MC×100.

Explanation

Given information:

The provided function for IQ level is IQ(M,C)=MC×100. Where, M is mental age and C is chronological age.

Formula used:

Consider the function z=f(x,y) then for the value of zx consider y to be constant and differentiate with respect to x and the value of zy consider x to be constant and differentiate with respect to y.

Calculation:

Consider the provided IQ function is,

IQ(M,C)=MC×100

Partially derivative of the function IQ(M,C)=MC×100 with respect to M.

IQM(M,C)=M(MC×100)=100CM(M)=100C

Substitute (M,C)=(12,10) in the derivative IQM(M,C)=100C.

IQM(12,10)=10010=10

Partially derivative of the function IQ(M,C)=MC×100 with respect to C

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