Math

Consider the function y = 3x5 – 25x3 + 60x + 1. Find the critical points of this function.

So I got 1 and 2 as the critical points..but I feel like I did something wrong, is this right?

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  1. I am sure you meant:
    y = 3x^5 - 25x^3 + 60x + 1
    dy/dx = 15x^4 - 75x^2 + 60
    = 0 for your critical values
    3x^4 - 15x^2 + 12 = 0
    x^4 - 5x^2 + 4 = 0
    (x^2 - 1)(x^2 - 4) = 0
    x^2 = 1 or x^2 = 4
    x = ± 1 OR x = ± 2

    sub in those values of x in the original to get the mataching y values of the critical points.

    Some would consider the inflection points in the list of critical points

    y'' = 60x^3 - 150x
    = 0 for points of inflection
    6x^3 - 15x = 0
    2x^3 - 5x = 0
    x(2x^2 - 5) = 0
    x = 0 or x = ± 5/2
    continue to find the points of inflection

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  2. So the points would be -1,-2,1,2?

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  3. no, points consist of ordered pairs of two numbers.
    ±1 and ±2 are the x's of the points.

    I told you what to do with those x's above, please read it.

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