# `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.

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Expert Answers

tiburtius | Certified Educator

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.

tiburtius | Certified Educator

Here is the image.