This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to find the production level that minimizes cost. To minimize the cost function, we need to find the value of x (production level) where the first derivative of the cost function is equal to zero. Step 1: Find the first derivative of the cost function C(x). The given cost function is C(x) = 2x^2 - 12x + 50. C'(x) = (d)/(dx)(2x^2 - 12x + 50) C'(x) = 4x - 12 Step 2: Set the first derivative to zero and solve for x. To find the critical point where the cost is minimized, we set C'(x) = 0: 4x - 12 = 0 4x = 12 x = (12)/(4) x = 3 Step 3: (Optional) Use the second derivative test to confirm it's a minimum. Find the second derivative of C(x): C''(x) = (d)/(dx)(4x - 12) C''(x) = 4 Since C''(x) = 4 > 0, the cost function has a local minimum at x=3. The production level that minimizes cost is 3 units. 3 units Last free one today — make it count tomorrow, or type /upgrade for unlimited.