Answer :
I am assuming it is f(x)=2x e^2x
2x times e raised to the 2x power, and not 2 times e raised to the 2x**
as it approaches infinity, your f(x) --> infinity
we can see by inspection, as 2x will approach inf, and e^(2x) will approach infinity even faster.
inf x inf = inf
as it approaches neg infinity, your f(x) --> 0
we can see by inspection, as 2x will approach neg inf, and e^(2x) will approach zero.
- inf x 0 = - 0
The minimum(or maximum) is given when the derivative = 0
Using the product rule,
f ' (x) = 2e^(2x) + 4x e(2x)
f ' (x) = 2e^(2x) ( 1 + 2x )
We find the roots
2e^(2x) will never equal 0
1 + 2x = 0, x = -1/2
The minimum value will be when x = -0.5
2x times e raised to the 2x power, and not 2 times e raised to the 2x**
as it approaches infinity, your f(x) --> infinity
we can see by inspection, as 2x will approach inf, and e^(2x) will approach infinity even faster.
inf x inf = inf
as it approaches neg infinity, your f(x) --> 0
we can see by inspection, as 2x will approach neg inf, and e^(2x) will approach zero.
- inf x 0 = - 0
The minimum(or maximum) is given when the derivative = 0
Using the product rule,
f ' (x) = 2e^(2x) + 4x e(2x)
f ' (x) = 2e^(2x) ( 1 + 2x )
We find the roots
2e^(2x) will never equal 0
1 + 2x = 0, x = -1/2
The minimum value will be when x = -0.5