Exam 8: Special Topics in Algebra

The vertex of a parabola occurs where the derivative of its equation is 0, so an equation associated with the equation of a parabola can be solved to find the x-coordinate of the vertex. Find the vertex of the parabola, given the equation of the parabola and its associated equation. -Between $x = - 2$ and $x = 10$ , the largest value of the expression $y = x ^ { 3 } - 12 x ^ { 2 } - 9$ occurs where $3 x ^ { 2 } - 24 x = 0$ . Of the values of $x$ that satisfy $3 x ^ { 2 } - 24 x = 0$ , which gives the maximum value of $y = x ^ { 3 } - 12 x ^ { 2 } - 9$ ?

The vertex of a parabola occurs where the derivative of its equation is 0, so an equation associated with the equation of a parabola can be solved to find the x-coordinate of the vertex. Find the vertex of the parabola, given the equation of the parabola and its associated equation. -Equation of parabola: $f ( x ) = 8 x ^ { 2 } + 32 x - 12$ ; associated equation: $0 = 16 x + 32$

Draw the graph of the equation. - $x ^ { 2 } + 3 y = 0$

Simplify the expression representing the derivative of a function. - $f ^ { \prime } ( x ) = \frac { x \left( 3 x ^ { 2 } \right) + \left( 4 x ^ { 2 } \right) ( x - 1 ) } { \left( x ^ { 2 } \right) ^ { 2 } }$

Find the sum of the first 7 terms of the geometric sequence with first term 3 and common ratio 1/2 .