Question Find the coordinates of any stationary points on these curves and state, giving reasons whether the points are maximum, minimum or points of inflexion.
y=x4+3x3
dxdy=4x3+9x2 put dy/dx = 0
x(4x2+9x)=0[br]x=0or4x2+9x=0 but doesn't 4x2+9x=0 has no real roots
but in the book the answer was (0,0) is inflexion which is right
but it also gave this answer (−39,−2562187) is a min
Question Find the coordinates of any stationary points on these curves and state, giving reasons whether the points are maximum, minimum or points of inflexion.
y=x4+3x3
dxdy=4x3+9x2 put dy/dx = 0
x(4x2+9x)=0[br]x=0or4x2+9x=0 but doesn't 4x2+9x=0 has no real roots
but in the book the answer was (0,0) is inflexion which is right
but it also gave this answer (−39,−2562187) is a min
how did the book get the second answer
Please help
I think you mean -9/4, as -9/3 is just -3. That's your first hint.
The second - just like you got x = 0, can you factorise the polynomial you say has no real roots? Or better yet, go back and do this in one step instead of two?
I think you mean -9/4, as -9/3 is just -3. That's your first hint.
The second - just like you got x = 0, can you factorise the polynomial you say has no real roots? Or better yet, go back and do this in one step instead of two?