Can anyone help me with this problem

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  (a) increasing: (-∞, 0) ∪ (0, 1); decreasing: (1, ∞)

  (b) maximum: (1, e^-3). No minimum.

Step-by-step explanation:

The derivative of the function is ...

  f'(x) = 3x^2(1 -x)e^(-3x)

This is zero at x=0, and positive elsewhere for values of x < 1. That is, ...

  the function is increasing for x < 1, except at x=0.

For x > 1, the derivative is negative, so ...

  the function is decreasing for x > 1.

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The derivative is zero at x=0 and x=1, so these are critical points. The point at x=0 is a flat spot, or point of inflection, as the derivative does not change sign there. The point at x=1 is a local/global maximum, as the derivative changes from positive (function increasing) to negative (function decreasing) at that point.

The function value at the maximum is f(1) = e^-3.

you should at least use a calculater

step-by-step explanation: