I'm having difficulty working out the maxima and minima of a number of easy equations, though I am grasping it quite well I'm still going wrong somewhere with the arithmetic, particularly where I'm trying to factor out the value(s) for x, after I have the derivative...

These are the two questions I am getting wrong so far...

(1) y = x + 1/x

y = x + x^-1

dy/dx = 1 - x^-2 = 0

1 = 1/x^2

x^2 = 1/1

x = square of 1

x = 1

d^2/dx^2 = 2x^-3

2(1)^-3 = 2

Minima

y = 2 + 1/2 = 2.5

My answer: MIN (2, 2.5)

But actual answer: MIN (1, 2) MAX (-1, -2)

(2) y = x^4 - 2x^2 + 1

dy/dx = 4x^3 - 4x = 0

4x(x - 1)(X + 1) = 0

x = 1 and -1

(here I think this is wrong)

d^2y/dx^2 = 12x^2 - 4

12(1)^2 - 4 = 8 Minimum

12(-1)^2 -4 = 8 Minimum

y = (1)^4 - 2(1)^2 + 1 = 1 - 2 + 1 = 0

y = (-1)^4 - 2(-1)^2 + 1 = 1 - 2 + 1 = 0

My answer: MIN (-1, 0) and MIN (1, 0) !!

Actual answer: MAX (0, 1), MIN (+/-1, 0)

It should be obvious where I've gone wrong but I'm not seeing it. I'd appreciate any help in setting me right. Thanks.