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Find the anti-derivative of \(\displaystyle f(x) = - x^{4} + 9 x^{3} - 5 x^{2} - 6 x + 6\).

Using the power rule on each term gives \(\displaystyle F(x) = - \frac{x^{5}}{5} + \frac{9 x^{4}}{4} - \frac{5 x^{3}}{3} - 3 x^{2} + 6 x + C\)

Download \(\LaTeX\)

\begin{question}Find the anti-derivative of $f(x) = - x^{4} + 9 x^{3} - 5 x^{2} - 6 x + 6$. 
    \soln{4cm}{Using the power rule on each term gives $F(x) = - \frac{x^{5}}{5} + \frac{9 x^{4}}{4} - \frac{5 x^{3}}{3} - 3 x^{2} + 6 x + C$}

\end{question}

Download Question and Solution Environment\(\LaTeX\)

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\begin{document}\begin{question}(10pts) The question goes here!
    \soln{9cm}{The solution goes here.}

\end{question}\end{document}

Find the anti-derivative of <img class="equation_image" title=" \displaystyle f(x) = - x^{4} + 9 x^{3} - 5 x^{2} - 6 x + 6 " src="/equation_images/%20%5Cdisplaystyle%20f%28x%29%20%3D%20-%20x%5E%7B4%7D%20%2B%209%20x%5E%7B3%7D%20-%205%20x%5E%7B2%7D%20-%206%20x%20%2B%206%20" alt="LaTeX: \displaystyle f(x) = - x^{4} + 9 x^{3} - 5 x^{2} - 6 x + 6 " data-equation-content=" \displaystyle f(x) = - x^{4} + 9 x^{3} - 5 x^{2} - 6 x + 6 " /> .

Using the power rule on each term gives <img class="equation_image" title=" \displaystyle F(x) = - \frac{x^{5}}{5} + \frac{9 x^{4}}{4} - \frac{5 x^{3}}{3} - 3 x^{2} + 6 x + C " src="/equation_images/%20%5Cdisplaystyle%20F%28x%29%20%3D%20-%20%5Cfrac%7Bx%5E%7B5%7D%7D%7B5%7D%20%2B%20%5Cfrac%7B9%20x%5E%7B4%7D%7D%7B4%7D%20-%20%5Cfrac%7B5%20x%5E%7B3%7D%7D%7B3%7D%20-%203%20x%5E%7B2%7D%20%2B%206%20x%20%2B%20C%20" alt="LaTeX: \displaystyle F(x) = - \frac{x^{5}}{5} + \frac{9 x^{4}}{4} - \frac{5 x^{3}}{3} - 3 x^{2} + 6 x + C " data-equation-content=" \displaystyle F(x) = - \frac{x^{5}}{5} + \frac{9 x^{4}}{4} - \frac{5 x^{3}}{3} - 3 x^{2} + 6 x + C " />