Question

STUCK ON THIS PROBLEM FOR 2 HRS, PLEASE HELP:

Answer 1

1. -0.2 ppm/mi
2. -0.025 ppm/mi

Explanation:

Given C(x) = 0.1/x², you want the rate of change of C(x) for x=1 and x=2. (C is ppm; x is miles.)

Derivative

The rate of change is given by the derivative of the function. The power rule applies.

`C(x)=(0.1)/(x^2)=0.1x^(-2)\\\\(dC)/(dx)=0.1(-2)x^(-3)=-(0.2)/(x^3)\qquad d(x^n)=n\cdot x^(n-1)dx`

(A) 1 Mile

For x=1, the rate of change is ...

C'(1) = -0.2/1³ = -0.2 . . . . ppm/mi

(B) 2 Miles

C'(2) = -0.2/2³ = -0.1(2/8) = -0.025 . . . . ppm/mi

__

Additional comment

Some graphing calculators work nicely with derivatives. The second attachment shows this. It doesn't "show work," but it gives you a way to check your result.