Question

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

$f(x)=5+\frac{1}{4}x - \frac{1}{2}x^{2}$

$x=$

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:

\(\frac{1}{4}\)