Question

Compute the derivative f'(a) algebraically. f(x)=x-2x^3

Answer 1

Set up your ratio and have at it. Let's see your best work.

Answer 2

Remember how to find the slope of a line?
\[\frac{y_2 - y_1}{x_2 - x_1}\]
The derivative formula is just a fancier version of that. Since \(y = f(x)\) we can say:
\[f'(x) = \lim_{x \rightarrow n} \frac{f(x) - f(n)}{x - n}\]