Calculus

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Find all critical points of the function.
f(x) = xe^3x

so x= ?

Show steps or tell me how I find them?

  • Calculus -

    A critical point is an interior point of an interval of the function at which f'(x)=0 or undefined.

    If the interval is not given, it is usually understood to be (-∞, ∞).

    f(x)=xe3x
    f'(x)=xe3x + e3x
    f'(x) is therefore defined within the interval (-∞, ∞).
    Now find x for which f'(x)=0
    f'(x)=0 when x=-(1/3) or e3x=0. The latter condition requires x to be outside the domain (x=-∞).
    Therefore the only critical point is x=-(1/3).

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