find the critical numbers of the function. (enter your answers as a comma-s answer does not exist, enter…

find the critical numbers of the function. (enter your answers as a comma-s answer does not exist, enter dne.)\n\n$f(x)=5+\\frac{1}{4}x - \\frac{1}{2}x^{2}$\n\n$x=$

find the critical numbers of the function. (enter your answers as a comma-s answer does not exist, enter dne.)\n\n$f(x)=5+\\frac{1}{4}x - \\frac{1}{2}x^{2}$\n\n$x=$

Answer

Explanation:

Step1: Differentiate the function

Use the power rule ((x^n)^\prime = nx^{n - 1}). For (f(x)=5+\frac{1}{4}x-\frac{1}{2}x^{2}), (f^\prime(x)=\frac{1}{4}-x).

Step2: Set the derivative equal to zero

Solve (f^\prime(x) = 0), i.e., (\frac{1}{4}-x=0). Add (x) to both sides: (x=\frac{1}{4}).

Answer:

(\frac{1}{4})