# f(t) = (3t + 2)/(t - 1), (0,-2) Find and evaluate the derivative of the function at the given point. Use a graphing utility to verify your result.

### Textbook Question

Chapter 2, 2.4 - Problem 69 - Calculus of a Single Variable (10th Edition, Ron Larson).
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tiburtius | High School Teacher | (Level 2) Educator

Posted on

First we differentiate the function using the following rule

(f/g)'=(f'g-fg')/g^2

f'(t)=(3(t-1)-(3t+2)\cdot1)/(t-1)^2=(3t-3-3t-2)/(t-1)^2=-5/(t-1)^2

Now we evaluate the derivative at 0.

f'(0)=-5/(0-1)^2=-5

In the image below blue is the graph of the function and red is the graph of its derivative.