Locate the critical points of the following function. Then use the Second Derivative Test to determine whether they correspond to local maxima or local minima, or if the test is inconclusive. \[ f(x)=\frac{1}{4} x^{4}-x^{3}-\frac{9}{2} x^{2}+27 x \] A. \( x= \) B. There are no critical points that are local maxima according to the Second Derivative Test. Identify all the critical points for which the Second Derivative Test is inconclusive. Select the correct choice below and fill in any answer boxes within your choice. A. \( x=\square \) B. There are no critical points for which the Second Derivative Test is inconclusive.

La derivada de la función \( f(x)=-2 x \) a. \( f^{\prime}(x)=-4 x \) b. \( f^{\prime}(x)=20 x^{3}+15 x^{2}+34 x-3 \) oc. \( f^{\prime}(x)=8 x^{3}+3 x^{2}-2 x \)

Consider the line \( y=\frac{2}{5} x \) What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? Slope of a parallel line:

Find all solutions of the equation in the interval \( [0,2 \pi) \) \[ (2 \cos x+1)(\csc x+1)=0 \] Write your answer in radians in terms of \( \pi \). If there is more than one solution, separate them with commas.

QUESTION 5 5.1 Determine the are length over the interval \( 0 \leq \theta \leq \frac{\pi}{2} \) for the curve with the following parametric equations:- \( \begin{array}{l}x=5 \cos ^{3} \theta \\ y=5 \sin ^{3} \theta\end{array} \)

Use partial fractions to calculate the following integrals: \( 3.1 \int \frac{x^{3}-2 x^{2}+1}{x^{2}\left(x^{2}+3\right)} d x \) \( 3.2 \int \frac{x^{3}-3 x^{2}+2 x-1}{x^{2}-4 x+4} d x \)