The function f(x) = e^x(x - 3) has a critical point at x =

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)

We want f'(x) = 0
e^x(x - 2) = 0

When x = 2, then f'(x) = 0