Asked by Alex
                Let F be the function defined by F(X)=12X to the 2/3 power minus 4X         Find the intervals of which F is increasing?  Find X & Y coordinates of all relative max. pts? Find X and Y Coordinates of all relative min pts? Find the intervals of which F is concave down?  Sketch a graph of F
            
            
        Answers
                    Answered by
            Reiny
            
    I read your statement as
f(x) = 12x^(2/3) - 4x
then
f '(x) = 8x^(-1/3) - 4
= 0 for max/min
8/x^(1/3) = 4
4x^(1/3) = 8
x^(1/3) = 2
x = 8
then f(8) = 12(8)^(2/3) - 4(8)
= 48 - 32
= 16
Can you take it from here?
remember that the function is concave up when the second derivative is positive and
concave down .....
    
f(x) = 12x^(2/3) - 4x
then
f '(x) = 8x^(-1/3) - 4
= 0 for max/min
8/x^(1/3) = 4
4x^(1/3) = 8
x^(1/3) = 2
x = 8
then f(8) = 12(8)^(2/3) - 4(8)
= 48 - 32
= 16
Can you take it from here?
remember that the function is concave up when the second derivative is positive and
concave down .....
                    Answered by
            Anonymous
            
    When the second derivative is negative 
    
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