Question

Help please?

Answer 1

limit definition for \(f'(x)\) is\[f'(x)=\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}\]have you tried it?

Answer 2

Im not sure how to do that equation

Answer 3

If \(f(x)=4.5x^2-3x+2\), then \(f(x+h)=4.5(x+h)^2-3(x+h)+2\). Agreed?

From the definition, you have
\[\begin{align*}f'(x)&=\lim_{h\to0}\frac{\overbrace{(4.5(x+h)^2-3(x+h)+2)}^{f(x+h)}-\overbrace{(4.5x^2-3x+2)}^{f(x)}}{h}\\\\
&=\lim_{h\to0}\frac{4.5x^2+9xh+4.5h^2-3x-3h+2-4.5x^2+3x-2}{h}\\\\
&\vdots\end{align*}\]

Answer 4

Yes

Answer 5

Simplify the fraction and take the limit.