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

Find the values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given point. \[ (\sqrt{6},-\sqrt{2}) \] \( \cos \alpha=\frac{-}{2} \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) tan \( \alpha=\square \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

Hallar la ecuación de la circunferencia con centro en el punto \( (7,1) \) y radio \( r=2 \) a. \( X^{2}+Y^{2}-7 X-2 Y+44=0 \) b. \( X^{2}+Y^{2}-14 X-2 Y+4=0 \)

\( evaluate(\sqrt {6-\sqrt {8)\times (\sqrt {8+\sqrt {15)}}}} \)

Find the least common denominator of \( \frac{7}{9 x+18} \) and \( \frac{5}{6 x} \)

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