Help with stat points (1 Viewer)

[dimzi]

Ok im having trouble with this bitch of a curve:

y=6x^2-x^3

I can only get the maximum, and not the minimum!

y'=0
0=12x-3x^2
3x^2=12x / both sides by x
3x=12
.:.x=4
stat point at (4,32)
y"=12-6x
=12-24
=-12
y"<0
max turning pt at (4,32)

But how the hell do I get the minimum? The answers say there is one at (0,0) but FIIK how to get it, so any help please?

 

[acmilan]

y'=0
0=12x-3x^2
3x^2=12x / both sides by x
3x=12
.:.x=4
stat point at (4,32)
y"=12-6x
=12-24
=-12
y"<0
max turning pt at (4,32)

But how the hell do I get the minimum? The answers say there is one at (0,0) but FIIK how to get it, so any help please?

Theres your problem, by dividing both sides by x you are eliminating a solution. Instead, factorise:

0=12x-3x²
3x(4-x) = 0
x = 0 or 4

y"=12-6x

At x = 0, y'' = 12 > 0 so theres a min at x = 0

 

[dimzi]

Oh I see...

Thanks heaps!