Final answer:
To find the critical numbers of the function f(x) = 10xe^(3x), calculate the derivative, set it equal to zero, and solve for x.
Step-by-step explanation:
The critical numbers of the function f(x) = 10xe^(3x) can be found by setting the derivative of the function equal to zero and solving for x.
Step 1: Calculate the derivative of f(x) using the product rule: f'(x) = 10e^(3x) + 30xe^(3x).
Step 2: Set f'(x) equal to zero and solve for x: 10e^(3x) + 30xe^(3x) = 0.
Step 3: Factor out e^(3x) to get 10 + 30x = 0. Solve this equation for x to find the critical numbers.