Question

Use Alternative Formula for Derivative to find the derivative for the following function:
f(x)= 3x^2-x+2

Answer 1

what is "alternate formula for derivatives"?

Answer 2

\[f'(x)=\lim_{z \rightarrow x} \frac{ f(z)-f(x) }{z-x }\]

Answer 3

\[f'(x)=\lim_{z \rightarrow x} \frac{ f(z)-f(x) }{z-x }\]
\[\lim_{z\to x}\frac{3z^2-z+2-(3x^2-x+2)}{z-x}\]
\[\frac{3z^2-z-3x^2+x}{x-z}\]
\[\frac{3(z^2-x^2)-(z-x)}{z-x}\] then factor the first term as the difference of two squares, cancel the \(z-x\) top an bottom and then replace \(z\) by \(x\)