Help with HW I have too much?

Question

My teacher gave the entire class a huge packet to complete because the class did bad on the test (I did well). I dont have enough time to finish this and all of my other HW, can you do some of the following.
State whether the critical point is maximum, minimum, or point of inflection

1. y= x^2 - 6x +1; x=3
2. x^2 - 2x -6; x=1
3. x^4 +3x^2-5;x=0
4.x^5-2x^3-2x^2;x=0
5.x^3+x^2-x;x=-1
6.2x^3+4; x=0

if you can do atleast one of them that would be good. I still have more HW to finish before the fight (Mayweather Hatton)

Tom it didnt I need to know whether its max min or point of inflection. So far i have the first 3 and the last one. need 4/5

Answer 1

1. y = x^2-6x+ 1 ; x=3
The axsx of symmetry = -b/2a = - -6/2= 3
Since the x^2 is positive, we have a minimnum at x =3

2. y = x^2 -2x -6; x =2
Same as problem 1 , minimum at x= 1

3. y =x^4 +3x^2 -5;x =0
dy/dx = 4x^3 +6x =0
2x( 2x^2+3)=0
So x = 0 is a minimum since f(0)= -5 and F(+/-1) = -1

Do rest same way

Answer 2

1. y = x^2 - 6x + 1
y = 3^2 - 6(3) + 1
y = 9 - 6(3) + 1
y = 9 - 18 + 1
y = -9 + 1
y = -8

2. x^2 - 2x - 6
1^2 - 2(1) - 6
1 - 2(1) - 6
1 - 2 - 6
-1 - 6
-7

3. x^4 + 3x^2 - 5
0^4 + 3(0)^2 - 5
0 + 3(0) - 5
0 + 0 - 5
-5

4. x^5 - 2x^3 - 2x^2
0^5 - 2(0)^3 - 2(0)^2
0 - 2(0) - 2(0)
0 - 0 - 0
0

5. x^3 + x^2 - x
1^3 + 1^2 - 1
1 + 1 - 1
2 - 1
1

6. 2x^3 + 4
2(0)^3 + 4
2(0) + 4
0 + 4
4

Hope this helps!