The critical points of a function f(x) = x^4*e^(-7x) have to be determined. The x-coordinates of the points are given by the solution of f'(x) = 0

f'(x) = 4x^3*e^(-7x) - 7*x^4*e^(-7x)

4x^3*e^(-7x) - 7*x^4*e^(-7x) = 0

=> e^(-7x)*x^3*(4 - 7x) = 0

=> x = 0 and x = 4/7

**The critical points of the function f(x) = x^4*e^(-7x) are at x = 0 and x = 4/7**

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