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10242010  #1 
Join Date: Mar 2010
Posts: 9

Rates of change question
Use an algebric strategy to verify that the point given for each function is either a maximum or a minimum.
x^33x ; (1, 2) so i tried finding the instantaneous rate of change before 1 and after 1 to see if its a maximum or a minimum, since if its a local max before 1 would be positive and after would be negative but i couldn't reach the solution in the back of the book. any help would be appreciated. the formula i used was the difference quotient. 
11032010  #2  
Join Date: Mar 2010
Posts: 9

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01062011  #3 
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01072011  #4  
Join Date: Nov 2010
Posts: 36

Quote:
Here are my thoughts: f(x) = x^3  3x; verify point (1,2) f '(x) = 3x^2 3 For max or min f '(x) = 0 so we get: 3x^2 3 = 0 (divide this though by 3 we get next line) x^2 1 = 0 then factorising we get (x + 1) (x  1) = 0 so x = 1 or x = 1 Substituting this back into the first eqn f (x) we can get the Y coordinates and determine whether local max or min. so f (1) = (1)^3 3(1) = 1 + 3 = 2 so coordinates are (1, 2) = Y max and f (1) = (1)^3 3(1) = 1 3 = 2 so coordinates are (1 , 2) = Y min Remember these are local max and mins not the highest or lowest points on the curve of f (x) = x^3  3x. See diagram of curve from x = 3 to x = 3 for confirmation. Hope this is of use for someone 

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