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Need help computing the derivative of a function using a particular definition

Hello,

Our instructor included a homework problem that requires me to use to use a particular definition to compute the derivative, but he never went over the definition in class, and our textbook doesn't use it in any of their examples because the normal derivative definition is much more widely used. Anyways, I have included the function and the definition I need to use in the image below. If you can walk me through the steps I would really appreciate it. To be honest, the only part I know how to plug into the definition is the f(x), but I have no idea what to plug in for f(a) or x-a. Thank you for your help!

Attachment 26732

Danni

Re: Need help computing the derivative of a function using a particular definition

You set a=3. So $\displaystyle f'(3) = \lim_{x \to 3} \frac{f(x)-f(3)}{x-3} = \lim_{x \to 3} \frac{4x^2 - x - 33}{x-3}$ since $\displaystyle f(3)= 4 \cdot 3^2 - 3 = 33$.

To take the limit, notice that you can factor the numerator....

- Hollywood

P.S. That Definition 6 is the same as the standard definition if you replace x and a with x+h and x. It's a little confusing since "new x" is different from "old x".

Re: Need help computing the derivative of a function using a particular definition

You are wonderful, hollywood. Thank you so much for laying it out so simply. After I got 33, I had no idea how that was supposed to help me find the derivative. Thanks again!!