en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

f(x)=3^x-54x+135

Solution

f (x) = 3^{x} - 54 x + 135

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq 3^{\frac{l n ( \frac{54}{l n ( 3 )} )}{l n ( 3 )}} - \frac{54 ln ( \frac{54}{l n ( 3 )} )}{ln ( 3 )} + 135

X Intercepts : - \frac{2 W _{- 1} ( - \frac{e ^{\frac{5 l n ( 3 )}{2}} l n ( 3 )}{54} ) - 5 ln ( 3 )}{2 ln ( 3 )}, 0, - \frac{2 W _{0} ( - \frac{e ^{\frac{5 l n ( 3 )}{2}} l n ( 3 )}{54} ) - 5 ln ( 3 )}{2 ln ( 3 )}, 0, Y Intercepts : (0, 136)

Asymptotes : None

Extreme Points : Minimum \frac{ln ( \frac{54}{l n ( 3 )} )}{ln ( 3 )}, 3^{\frac{l n ( \frac{54}{l n ( 3 )} )}{l n ( 3 )}} - \frac{54 ln ( \frac{54}{l n ( 3 )} )}{ln ( 3 )} + 135

+1

Interval Notation

Domain : (- \infty, \infty)

Range : 3^{\frac{l n ( \frac{54}{l n ( 3 )} )}{l n ( 3 )}} - \frac{54 ln ( \frac{54}{l n ( 3 )} )}{ln ( 3 )} + 135, \infty

Solution steps

Domain of

3^{x} - 54 x + 135 : - \infty < x < \infty

Range of

3^{x} - 54 x + 135 : f (x) \geq 3^{\frac{l n ( \frac{54}{l n ( 3 )} )}{l n ( 3 )}} - \frac{54 ln ( \frac{54}{l n ( 3 )} )}{ln ( 3 )} + 135

Axis interception points of

3^{x} - 54 x + 135 :

X Intercepts

: - \frac{2 W _{- 1} ( - \frac{e ^{\frac{5 l n ( 3 )}{2}} l n ( 3 )}{54} ) - 5 ln ( 3 )}{2 ln ( 3 )}, 0, - \frac{2 W _{0} ( - \frac{e ^{\frac{5 l n ( 3 )}{2}} l n ( 3 )}{54} ) - 5 ln ( 3 )}{2 ln ( 3 )}, 0,

Y Intercepts

: (0, 136)

Asymptotes of

3^{x} - 54 x + 135 :

None

Extreme Points of

3^{x} - 54 x + 135 :

Minimum

\frac{ln ( \frac{54}{l n ( 3 )} )}{ln ( 3 )}, 3^{\frac{l n ( \frac{54}{l n ( 3 )} )}{l n ( 3 )}} - \frac{54 ln ( \frac{54}{l n ( 3 )} )}{ln ( 3 )} + 135

Popular Examples

y = tan^{4} (x^{3} + 2)

y=((sqrt(x)+1)/((sqrt(x))))^2

y = (\frac{x + 1}{( x )})^{2}

y = 5 cos (3 x) + 4

f(x)=(x^{50}+1)/((x^{50))}

f (x) = \frac{x ^{50} + 1}{( x ^{50} )}

f(x)=sqrt(x^2+1)*(x^3+2x)

f (x) = x^{2} + 1 \cdot (x^{3} + 2 x)

Frequently Asked Questions (FAQ)

What is the f(x)=3^x-54x+135 ?
The f(x)=3^x-54x+135 is