Find local max & min of 2 + f(2x2+ 3X +1) ?

• it should be -3x
• 11 years agoHelpfull: Yes(1) No(7)
• f'(x) = 3x^2 + 4x
  
  3x^2 + 4x = 0
  x(3x + 4) = 0
  x = 0 or x = 4/3
  
  f(0) = 0^3 = 2 * 0^2 + 1 = 1
  f(4/3) = (4/3)^3 - 2 * (4/3)^2 + 1 = 64/27 - 32/9 + 1
  = 64/27 - 96/27 + 27/27 = -5/27
  
  f(4/3) < f(0) so (0,1) is a local maximum and (4/3,. -5/27) is the local minimum.
• 9 years agoHelpfull: Yes(1) No(0)
• f`(x)=4x+3
  then equate this equation to 0,
  so,4x+3=0
  4x=-3
  x=-3/4
  then,
  for f(0)=2+2*(0)^2+3*0+1
  =2+0+0+1
  =3
  f(-3/4)=2+2*(-3/4)^2+3*(-3/4)+1
  =2+2*9/16-9/4+1
  =2+9/8-9/4+1
  =15/8
  so here f(-3/4)
• 8 years agoHelpfull: Yes(0) No(0)