Find the critical numbers of the function. (enter your answers as a comma-separated list. if an answer does not exist, enter dne.) f(x) = 6 + 1 4 x − 1 2 x2

f(x) = 6 + 14x - 12x^2    (please use "^" to denote exponentiation)

To find the critical numbers, find the first derivative dy/dx, set it = to 0, and solve the resulting equation for x:

f '(x) = 0 + 14 - 24x = 0    => 24x = 14   =>    x = 14/24 = 7/12

There is just one critical number here, and it is x = 7/12.  Find the corresponding y-value.  At this point, the tangent line to the graph is horizontal.