(Solved): if \( = \) \( x \) \( 6= \) (c) Uue the fact that at \( x=109 \) the helde in f and the path is Pu ...

if \( = \) \( x \) \( 6= \) (c) Uue the fact that at \( x=109 \) the helde in f and the path is Purtarathal to detertrine the veven or a and \( b \), \( 1= \) \( b= \) Make a sign diagram for the derivative of the rational function. \[ f(x)=\frac{3 x+6}{x-2} \] Find all relative extreme points. (If an answer does not exist, enter DNE.) relative \( \max (x, y)= \) relative \( \min (x, y)= \) Find all asymptotes. (Enter your answers as a comma-separated list. If an a vertical asymptote(s) \( x= \) horizontal asymptote(s) \( \quad y= \) Sketch the graph of the rational function. Make a sign diagram for the derivative of the function. \[ f(x)=x^{3}-3 x^{2}-9 x+5 \] Find all open intervals of increase and decrease. (Enter your answers using interval notation.) increase decrease Sketch the graph of the function. A plane is to take off and reach a level cruising altwide of h miles after a horizontal distance of 100 miles, as shown in the following diagram, Find a polynomial fight path of the form \( f(x)=a x^{2}+b x^{2}+c x+d b y \) follewing steps (a) to \( (d) \) to determine the constants \( a, b, c \), and \( d \). (Assume \( h=8 \) miles.) (a) Use the fact that the plane is on the grnund at \( x=0[t h a t i a, f(0)=0] \) to determine the value of \( d \). 4 (b) Use the fact that the path is horizontal at \( x=o f t=t \) is, \( f Y 0)=0) \) to detecmine the velue of \( c \) \( c= \) (c) Use the fact that at \( x \) - 100 the height is 8 ard the path is horiruntal to determine the values of a and 0 . \( 5= \) Gtate the fiencuon ful that ruu have determined \( f(x)= \) (d) Wse a graphing caicututer to uraph your function on the nindow \( (0,100) \) by \( (0 \), of te verity its shape.