# Solving turning points I'm wondering if I'm right or wrong. question is Apply differentiation to determine the co-ordinates of the turning points on the graph Y=X3-6X2+9x
and finf max and min turning points

SteamKing
Staff Emeritus
Homework Helper
View attachment 77039 I'm wondering if I'm right or wrong. question is Apply differentiation to determine the co-ordinates of the turning points on the graph Y=X3-6X2+9x
and finf max and min turning points

When you are solving the equation x2 - 4x + 3 = 0, you made a silly mistake.

This equation has two factors, namely (x - 3) and (x - 1). Re-writing x2 - 4x + 3 = (x - 3)(x - 1) = 0. By setting each factor equal to zero independently, you can make the equation true; thus x - 3 = 0 or x - 1 = 0. The solutions you have, x = -3 and x = -1, are incorrect.

When you are solving the equation x2 - 4x + 3 = 0, you made a silly mistake.

This equation has two factors, namely (x - 3) and (x - 1). Re-writing x2 - 4x + 3 = (x - 3)(x - 1) = 0. By setting each factor equal to zero independently, you can make the equation true; thus x - 3 = 0 or x - 1 = 0. The solutions you have, x = -3 and x = -1, are incorrect.

Ok I did have trouble they're , i'm a long time away from this type of stuff and trying to remember from 25 years ago. Where should I go fro here so?

SteamKing
Staff Emeritus
Homework Helper
Correct the solutions you have and work from there. All of your work past this point must be checked again using the correct solutions.

I used quadratic formula and got x=1,x=3
sub in x=3
Y=x3-6x2+9
Y=(3)3-6(3)2+9
Y=27-54+9
Y=-18

sub in x=1
Y=(1)3-6(1)2+9
Y=1-6+9
Y=4

dy/dx=3x2-12x+9

d2y/dx2=6x-12

X=1, 6(1)-12=-6
X=3, 6(3)-12=6

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