anonymous one year ago Help please?

1. anonymous

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

2. anonymous

Im not sure how to do that equation

3. anonymous

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*}

4. anonymous

Yes

5. mathstudent55

Simplify the fraction and take the limit.