What is the extreme f(x)=-6x^2e^{-x}-4 ?

The extreme f(x)=-6x^2e^{-x}-4 is Maximum(0,-4),Minimum(2,-(24)/(e^2)-4)

extreme f(x)=-6x^2e^{-x}-4

extreme points

f (x) = - 6 x^{2} e^{- x} - 4

Maximum (0, - 4), Minimum (2, - \frac{24}{e ^{2}} - 4)

Solution steps

f^{'} (x) = 6 e^{- x} x (x - 2)

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 0

into

- 6 x^{2} e^{- x} - 4 : - 4

Maximum (0, - 4)

Plug

x = 2

into

- 6 x^{2} e^{- x} - 4 : - \frac{24}{e ^{2}} - 4

Minimum (2, - \frac{24}{e ^{2}} - 4)

Maximum (0, - 4), Minimum (2, - \frac{24}{e ^{2}} - 4)

f (x) = 2.2 + 2.6 x - 0.8 x^{2}

f (x) = - 4 x^{3} + 12 x^{2} + 36 + 3

f (x) = 3^{\frac{2}{3}} - 2 x (- 1.1)

f (x) = - 0.001 x^{2} + 6 x - 1900

h (x) = 5 (x - 1)^{\frac{2}{3}}, 0 \leq x \leq 2

What is the extreme f(x)=-6x^2e^{-x}-4 ?
The extreme f(x)=-6x^2e^{-x}-4 is Maximum(0,-4),Minimum(2,-(24)/(e^2)-4)