What is the f(x)=e^{4x}+4e^{4x}x ?

f(x)=e^{4x}+4e^{4x}x

f (x) = e^{4 x} + 4 e^{4 x} x

Domain : - \infty < x < \infty

Range : f (x) \geq - \frac{1}{e ^{2}}

X Intercepts : (- \frac{1}{4}, 0), Y Intercepts : (0, 1)

Asymptotes : Horizontal y = 0

Extreme Points : Minimum (- \frac{1}{2}, - \frac{1}{e ^{2}})

Interval Notation

Domain : (- \infty, \infty)

Range : [- \frac{1}{e ^{2}}, \infty)

Solution steps

Domain of

e^{4 x} + 4 e^{4 x} x : - \infty < x < \infty

Range of

e^{4 x} + 4 e^{4 x} x : f (x) \geq - \frac{1}{e ^{2}}

Axis interception points of

e^{4 x} + 4 e^{4 x} x :

X Intercepts

: (- \frac{1}{4}, 0),

Y Intercepts

: (0, 1)

Asymptotes of

e^{4 x} + 4 e^{4 x} x :

Horizontal

: y = 0

Extreme Points of

e^{4 x} + 4 e^{4 x} x :

Minimum

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

x \to \infty lim (\frac{ln ^{3} ( x )}{100 3 x})

\int 12 x e^{- 3 x} d x

\frac{d}{d x} (x co x (x))

t an g e n t f (x) = 2 + \frac{1}{x}, (4, 2.25)

\int_{- 2}^{2} (x^{3} - 2 x + 3) d x