Questions: f(x)=6+3x-5x^2

Transcript text: $f(x)=6+3x-5x^{2}$

Solution

Solution Steps

Step 1: Compute the Derivative

The function is given by $ f(x) = 6 + 3x - 5x^2 $. To find the critical numbers, we first compute the derivative of the function: \[ f'(x) = 3 - 10x \]

Step 2: Set the Derivative to Zero

Next, we set the derivative equal to zero to find the critical points: \[ 3 - 10x = 0 \] Solving for $ x $, we get: \[ 10x = 3 \quad \Rightarrow \quad x = \frac{3}{10} \]

Step 3: Identify Critical Numbers

The critical number of the function $ f(x) $ is $ x = \frac{3}{10} $.