W wolf7 Member Joined Oct 10, 2005 Messages 49 Gender Male HSC 2006 Nov 21, 2005 #1 find any stationary points on the curve y=(4x^2-1)^4 and determine their nature also the curve y = ax^3 +bx^2 - x +5 has a point of inflexion at (1,-2) find the values of a and b
find any stationary points on the curve y=(4x^2-1)^4 and determine their nature also the curve y = ax^3 +bx^2 - x +5 has a point of inflexion at (1,-2) find the values of a and b
klaw Member Joined Jul 19, 2005 Messages 683 Gender Male HSC 2006 Nov 21, 2005 #2 y'=32x(4x^2-1)^3=32x[(2x+1)(2x-1)]^3 When y'=0, x=0 or +-1/2 When x=0, y=1 When x=1/2, y=0 When x=-1/2, y=0 Then just use product rule to find y'' and sub the x values in to determine their nature.
y'=32x(4x^2-1)^3=32x[(2x+1)(2x-1)]^3 When y'=0, x=0 or +-1/2 When x=0, y=1 When x=1/2, y=0 When x=-1/2, y=0 Then just use product rule to find y'' and sub the x values in to determine their nature.
klaw Member Joined Jul 19, 2005 Messages 683 Gender Male HSC 2006 Nov 21, 2005 #3 y=ax^3+bx^2-x+5 y'=3ax^2+2bx-1 y''=6ax+2b When x=1, y=-2 .:-2=a+b-1+5 .:a+b=-6 When x=1, y''=0 .:6a+2b=0 Then solve simultaneously
y=ax^3+bx^2-x+5 y'=3ax^2+2bx-1 y''=6ax+2b When x=1, y=-2 .:-2=a+b-1+5 .:a+b=-6 When x=1, y''=0 .:6a+2b=0 Then solve simultaneously
W wolf7 Member Joined Oct 10, 2005 Messages 49 Gender Male HSC 2006 Nov 21, 2005 #4 thanx, i get the question now
