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    because a quadratic only has two solutions?
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    (Original post by UCASLord)
    Yes, but a cubic can have 3 solutions. How do I know that I'm not missing a solution?
    A cubic can have three solutions, but what you are finding by differentiating is the MINIMUM and MAXIMUM POINTS. A cubic (any cubic) will only have TWO minimum and maximum points, which are points that have a gradient of 0.
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