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how do you find relative max/min without derivatives?

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To obtain the relative maximum(s) and minimum(s), you have to use that derivative formula you have and set it equal to 0 or undefined. Since there is no denominator in the derivative, you can ignore the "set it equal to undefined" part. So, for 3x^2 - 12x, you would first factor out the 3x, to get 3x(x-4). Next, set this equal to 0. 3x(x-4) = 0 You should get x=0, 4. These are called critical #'s. Next, you make a number line of any length which include these 2 numbers as points on them: <--O---O---> Circle 1 is x=0, second circle is x=4. Now test the intervals for the # line (test x<0, 04). To test, choose any value in the interval and plug it in to the derivative function. On the number line, mark whether the intervals are positive or negative. + - + <--O--O--> Circle 1 is x=0, second circle is x=4. Since f '(the derivative function) represents the slope of the tangent, you know there is a min when the slope changes from negative to positive, so 4 is your min. (Plug this into f(x) to get the y value of this point.) Also, when slope goes from + to -, you have a max, so 0 is the max. (Plug this in to f(x) to get the y-value of the point.) Hope this helps.
@Koikkara ''without derivatives''
Only method i see without derivatives is Hit and Trial!

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