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Question

# Use a computer algebra system to find the second derivative of the function. \$f(x)=6 x^2 e^{-x / 3}$

Solution

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Given:

\begin{aligned} f(x)=6x^2e^{-\frac{x}{3}} \end{aligned}

Using a computer algebra system, we found that:

\begin{aligned} f'(x)&=-2\left(x-6\right)xe^{-\frac{x}{3}}\\ f''(x)&=\frac{\left(2x^2-24x+36\right)e^{-\frac{x}{3}}}{3} \end{aligned}

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