Question

(70 points)

To approximate unemployment for the years following 1990, an economist used the function f(x) = -0.26x2 + 1.2x + 5.7, where x is the number of years since 1990 and f(x) is the percentage of Americans in the labor force who were unemployed.

Select the function that defines the rate of change in the unemployment rate.

A. f'(x) = -0.083x^3 +0.6x^2 + 5.7x +C
B. f'(x) = -0.26x + 1.2
C. f'(x) = -0.52x + 1.2
D. f'(x) = 1.2x +5.7

Answer 1

f(x) = -0.26x^2 + 1.2x + 5.7

differentiate by x

f'(x) = -0.26*2x + 1.2

= -0.52x + 1.2

ans is C

Answer 2

`f(x) = -0.26x^2 + 1.2x + 5.7\\\\\\f'(x)=(-0.26x^2 + 1.2x + 5.7)'=(-0.26x^2)'+(1.2x)'+(5.7)'=\\\\=-0.26(x^2)' + 1.2(x)' + (5.7)'=-0.26\cdot(2x) + 1.2\cdot1+0=\\\\=\boxed{-0.52x+1.2}`

Answer C)