To approximate unemployment for the years following 1990, an economist used the function f(x) = -0.26x^2 + 1.2x + 5.7, where x is the number of years since 1990
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) = 1.2x + 5.7
C.)f '(x) = -0.26x + 1.2
D.)f '(x) = -0.52x + 1.2
Do you know how to take the derivative of a polynomial?
That is what you are supposed to do wth this one.
If you don't know, read this:
http://www.freemathhelp.com/derivative-of-polynomial.html
To find the rate of change in the unemployment rate, we need to take the derivative of the function f(x) with respect to x.
Given f(x) = -0.26x^2 + 1.2x + 5.7, we can find f'(x) by differentiating each term separately:
f'(x) = (-0.26x^2)' + (1.2x)' + (5.7)'
The derivative of x^n, where n is a constant, is nx^(n-1). Applying this rule:
f'(x) = -0.26(2x^(2-1)) + 1.2(1x^(1-1)) + 0
Simplifying:
f'(x) = -0.52x + 1.2
Therefore, the correct function that defines the rate of change in the unemployment rate is
D.) f '(x) = -0.52x + 1.2.
So, the rate of change in the unemployment rate is -0.52x plus 1.2.