identify weather the function y=3(x-2)^2+11 has a minimum or maximum value. Then state the value.

At minimum or maximum, slope = 0.

=> dy/dx = 6 ( x - 2 ) = 0

=> x = 2

=> minima or maxima at x = 2

To find which one, double differentiate to get :

d/dx ( dy/dx ) = 6 which is > 0.

Therefore, at x = 2 we have a minimum with value = 11

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