critical point

The function f(x) = e^x(x - 3) has a critical point at x = The critical point is where the derivative equals 0. We multiply through for f(x) to get: f(x) = xe^x - 3e^x Using the product rule on the first term f'g + fg', we get: f'(x) = xe^x + e^x - 3e^x f'(x) = xe^x -2e^x f'(x) = e^x(x - 2)...