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
Question
Answer:
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.
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