The Student Room Group

C2 Differentiation Question

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 y=x^{4}+3x^{3}

dydx=4x3+9x2 \frac{\mathrm{d} y}{\mathrm{d} x} = 4x^{3}+9x^{2}
put dy/dx = 0

x(4x2+9x)=0[br]x=0or4x2+9x=0 x(4x^{2}+9x)=0[br] x=0 or 4x^{2}+9x=0
but doesn't 4x2+9x=0 4x^{2}+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 (93,2187256) (-\frac{9}{3}, -\frac{2187}{256}) is a min

how did the book get the second answer

Please help
take a factor of x^2 out instead of x from your dy/dx :smile:
Original post by bigmansouf
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 y=x^{4}+3x^{3}

dydx=4x3+9x2 \frac{\mathrm{d} y}{\mathrm{d} x} = 4x^{3}+9x^{2}
put dy/dx = 0

x(4x2+9x)=0[br]x=0or4x2+9x=0 x(4x^{2}+9x)=0[br] x=0 or 4x^{2}+9x=0
but doesn't 4x2+9x=0 4x^{2}+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 (93,2187256) (-\frac{9}{3}, -\frac{2187}{256}) 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?
(4x^2+9x) = 0
x(4x+9) = 0
x = -9/4
Reply 4
Original post by SeanFM
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?


woow thanks
Reply 5
Original post by Razzamataz179
(4x^2+9x) = 0
x(4x+9) = 0
x = -9/4


thanks im rushing tonight to finish differentiation
i didnt seee my own mistakes
Cool, I remember doing this sort of question in the FSMQ Additional maths :smile: Good old dy/dx
Reply 7
Original post by bigmansouf
thanks im rushing tonight to finish differentiation
i didnt seee my own mistakes


What year are you in?
Reply 8
Original post by SCAR H
What year are you in?


im just doing it for myself i want to do computer science in uni
i changed my career
i didnt want to do economics any more

Quick Reply

Latest