Let f be a function whose Maclaurin series expansion.f(x)=3+12x+24x2+32x3+…Explain how you can determine f'(0), f''(0), and f'''(0) simply by analyzing the oefficients of x, x2, and x3 in the given representation and without directly alculating f'(x), f''(x), and f'''(x) from the representation above.

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Let f be a function whose Maclaurin series expansion.f(x)=3+12x+24x2+32x3+…Explain how you can determine f&#039;(0), f&#039;&#039;(0), and f&#039;&#039;&#039;(0) simply by analyzing the oefficients of x, x2, and x3 in the given representation and without directly alculating f&#039;(x), f&#039;&#039;(x), and f&#039;&#039;&#039;(x) from the representation above.

Nathanael Webber · Accepted Answer

A Macluarin series is an enlargement of the Taylor series by a function around 0.f(x)=f(0)+f′(0)x+f&amp;nbsp;″(0)2!n2+f&amp;nbsp;‴(0)3!n3+…Given that&amp;nbsp;f(x)=3+12x+24x2+32x3+...Comparing with the above definition we get f&#039;(0)12,f&amp;nbsp;″(0)26=24⇒f&amp;nbsp;″(0)=48f&amp;nbsp;‴(0)3!=32⇒f&amp;nbsp;‴(0)=32⋅6=192f&#039;(0)=coefficient of&amp;nbsp;x∈f(x)f&#039;&#039;(0)=2! x coefficient of&amp;nbsp;x2∈f(x)f&#039;&#039;&#039;(0)=3! x coefficient of&amp;nbsp;x3∈f(x)&amp;nbsp;

Jeffrey Jordon · Accepted Answer

Explanation is on photo:

Let f be a function whose Maclaurin series expansion. f(x)=3+12x+24x^2+32x^3+... Explain how you can determine f'(0), f''(0), and f'''(0) simply by an

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