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The first question of x ^ 3-3ax ^ 2-9a ^ 2x-a ^ 3, when a = 1, is to find the extremum. The answer is derivative. I can't understand it, I study literature, so I'd better hurry up and have no requirements. There should be no problems for people above grade three in senior high school, so I don't give too many rewards. To promote the ideological and moral construction, we should take serving the people as the core, collectivism as the principle, focus on improving the sense of honesty, love the motherland, love the people, love labor, love science, love socialism as the basic requirements, and social morality and professional ethics as the core, Focusing on family virtues and personal morality, we should carry out the party's basic theory in depth~
I'm also a sophomore in high school, but I taught myself derivative out of interest. If you don't touch derivative, it's really hard for me to make it clear to you, because the principle can't be made clear in two or three sentences
But I still want to say, because at the beginning I also like derivative, but no one told me
The derivative of a function refers to the slope of the tangent of the function. For example, the derivative of y = x is 1, which is a straight line, and the slope is constant. It should be easier to understand. But the derivative of y = x & sup2; is variable (that is, the slope is variable). The slope of y = x & sup2; is 2x, and the slope of y = x & sup3; is 3x & sup2 Anyway, as long as it's not a straight line, then the slope of this function at point x changes with the change of X. derivative studies these things
To find the derivative of a function, there are many types of functions, so there are many formulas. I will not list them one by one. The problem you give is to use such a formula: the derivative of x ^ n is n * x ^ (n-1), that is, put the exponent in front of X, multiply X by a coefficient n, and then subtract the original exponent by one. In this way, it is not difficult to understand why the derivative of y = 2x & sup2; is 4x, and y = x & sup3; Is the derivative of 3 x & sup2~
Back to your question, when a = 1, y = x & sup3; - 3x & sup2; - 9x-1
The derivative is y '= 3x & sup2; - 6x-9 (because the derivative of the constant is 0, so - 1 is absent)
Then I'll explain what the extreme value is. As the name implies, it is a very large or small value. The extreme value is different from the maximum value. The maximum value is the maximum or minimum of Y in any range of X in the whole function. The extreme value is the maximum or minimum of X in a small range. When a function fluctuates, the rising or falling trend changes every time, It's when there are extremums. Of course, there are many extremums,
Let the derivative of a function be 0, and then solve the equation, all the solutions obtained are extremum. You can understand that when the derivative is 0, the slope is 0, that is to say, the tangent of a certain point is parallel to the X axis, and this point is of course extremum, because it has no upward or downward trend
Let y '= 3x & sup2; - 6x-9 = 0
Then x = (3 ± 3 √ 3) / 2
Then these two values of X are extremum
RELATED INFORMATIONS
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