What is the extreme f(x)=(x^3-5x^2+11x-11)e^x ?

The extreme f(x)=(x^3-5x^2+11x-11)e^x is Minimum(0,-11),Saddle(1,-4e)

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extreme f(x)=(x^3-5x^2+11x-11)e^x

extreme points

f (x) = (x^{3} - 5 x^{2} + 11 x - 11) e^{x}

Minimum (0, - 11), Saddle (1, - 4 e)

Solution steps

f^{'} (x) = e^{x} x (x - 1)^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = 0

into

(x^{3} - 5 x^{2} + 11 x - 11) e^{x} : - 11

Minimum (0, - 11)

Plug

x = 1

into

(x^{3} - 5 x^{2} + 11 x - 11) e^{x} : - 4 e

Saddle (1, - 4 e)

Minimum (0, - 11), Saddle (1, - 4 e)

What is the extreme f(x)=(x^3-5x^2+11x-11)e^x ?
The extreme f(x)=(x^3-5x^2+11x-11)e^x is Minimum(0,-11),Saddle(1,-4e)