What is the extreme f(x)=25x^2e^{2x}-16 ?

The extreme f(x)=25x^2e^{2x}-16 is Maximum(-1,(25)/(e^2)-16),Minimum(0,-16)

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extreme f(x)=25x^2e^{2x}-16

extreme points

f (x) = 25 x^{2} e^{2 x} - 16

Maximum (- 1, \frac{25}{e ^{2}} - 16), Minimum (0, - 16)

Solution steps

f^{'} (x) = 50 e^{2 x} x (x + 1)

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 1

into

25 x^{2} e^{2 x} - 16 : \frac{25}{e ^{2}} - 16

Maximum (- 1, \frac{25}{e ^{2}} - 16)

Plug

x = 0

into

25 x^{2} e^{2 x} - 16 : - 16

Minimum (0, - 16)

Maximum (- 1, \frac{25}{e ^{2}} - 16), Minimum (0, - 16)

What is the extreme f(x)=25x^2e^{2x}-16 ?
The extreme f(x)=25x^2e^{2x}-16 is Maximum(-1,(25)/(e^2)-16),Minimum(0,-16)