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**1. Homework Statement**

Given the following formula for distance, find the average velocity on the interval [1,3]

S(t) = t/(1+t^2)

**2. Homework Equations**

Vavg = (S(t0) - S(t1)) / (t0 - t1)

or

Vavg = (V0 + V1)/2

**3. The Attempt at a Solution**

I get two different answers and I need help understand why.

Vavg = (S(1) - S(3)) / (1-3)

Vavg = (1/2 - 3/10) / -2

Vavg = -2/20 = -1/10

Now using a different method, getting the instantaneous velocity at t = 1 and t = 3 by taking derivative of S(t) -> S'(t) = (1-t^2)/(1+t^2)^2

Vavg = (S'(1) + S'(3))/2

Vavg = (-8/100)/2 = (-2/25)/2 = -1/25

Why am I getting different averages here?? I don't understand what I'm doing wrong.

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