Classification of stationary points of functions?

Find and classify the stationary points of the following functions:

5x^3 - x^3 - x - 1

x^5 - x^4

(x^2) * (e^x)

I've worked them out already but just wanted to chekc my workings/answers against how others work them out...

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    1)

    f(x)=5x^3 - x^3 - x - 1

    f'(x)=15x^2 - 3x^2 - 1

    f''(x) = 30x -6x

    2)

    f(x) = x^5 - x^4

    f'(x) = 5x^4 - 4x^3

    f''(x) = 20x^3 - 12x^2

    3)

    f(x) = (x^2) * (e^x)

    f''(x) = (2x)(ex^(x-1))

    f''(x) = 2(x+1)(ex)^x-2

    So the answers would be

    1)

    f'(x)=15x^2 - 3x^2 - 1

    f'(x) = 0 when gradient = 0 aka stationary point

    15x^2-3x^2-1 = 0

    12x^2 = 1

    x^2 = 1/12

    x = (1/12)^0.5

    x = .22

    2)

    f'(x) = 5x^4 - 4x^3

    f'(x) = 0 when gradient = 0 aka stationary point

    5x^4 - 4x^3 = 0

    (5)(x)(x)(x)(x) - 4(x)(x)(x) =0

    Therefor x = 0, etc.

    3)

    f''(x) = (2x)(ex^(x-1))

    f'(x) = 0 when gradient = 0 aka stationary point

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