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STUCK ON THIS PROBLEM FOR 2 HRS, PLEASE HELP:

STUCK ON THIS PROBLEM FOR 2 HRS, PLEASE HELP:-example-1
User Dwight
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1 Answer

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Answer:

  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.

STUCK ON THIS PROBLEM FOR 2 HRS, PLEASE HELP:-example-1
User Nazmin
by
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