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anonymous
 one year ago
Help please?
anonymous
 one year ago
Help please?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0limit definition for \(f'(x)\) is\[f'(x)=\lim_{h \to 0} \frac{f(x+h)f(x)}{h}\]have you tried it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im not sure how to do that equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If \(f(x)=4.5x^23x+2\), then \(f(x+h)=4.5(x+h)^23(x+h)+2\). Agreed? From the definition, you have \[\begin{align*}f'(x)&=\lim_{h\to0}\frac{\overbrace{(4.5(x+h)^23(x+h)+2)}^{f(x+h)}\overbrace{(4.5x^23x+2)}^{f(x)}}{h}\\\\ &=\lim_{h\to0}\frac{4.5x^2+9xh+4.5h^23x3h+24.5x^2+3x2}{h}\\\\ &\vdots\end{align*}\]

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Simplify the fraction and take the limit.
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