SOLUTION: Find the slope of the curve 3x^2-y^2=12 if x=4.

3x² - y² = 12

6x - 2y = 0

6x(1) - 2y = 0
6x - 2y = 0
    -2y = -6x
        = 
        = 

To use that, we must find y when x = 4

  3x² - y² = 1
3(4)² - y² = 1 
 3*16 - y² = 1
   48 - y² = 1
       -y² = -47
        y² = 47
         y = 

        = , substitute (4,)
        = 
        = 

Edwin