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Popular Calculus >

f(x)=e^x-sqrt(x)-2

Solution

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

Solution

Domain : x \geq 0

Range : f (x) \geq e^{\frac{W _{0} ( \frac{1}{2} )}{2}} - \frac{W _{0} ( \frac{1}{2} )}{2} - 2

Y Intercepts : (0, - 1)

Asymptotes : None

Extreme Points : Maximum (0, - 1), Minimum \frac{W _{0} ( \frac{1}{2} )}{2}, e^{\frac{W _{0} ( \frac{1}{2} )}{2}} - \frac{W _{0} ( \frac{1}{2} )}{2} - 2

+1

Interval Notation

Domain : [0, \infty)

Range : e^{\frac{W _{0} ( \frac{1}{2} )}{2}} - \frac{W _{0} ( \frac{1}{2} )}{2} - 2, \infty

Solution steps

Domain of

e^{x} - x - 2 : x \geq 0

Range of

e^{x} - x - 2 : f (x) \geq e^{\frac{W _{0} ( \frac{1}{2} )}{2}} - \frac{W _{0} ( \frac{1}{2} )}{2} - 2

Axis interception points of

e^{x} - x - 2 :

Y Intercepts

: (0, - 1)

Asymptotes of

e^{x} - x - 2 :

None

Extreme Points of

e^{x} - x - 2 :

Maximum

(0, - 1),

Minimum

\frac{W _{0} ( \frac{1}{2} )}{2}, e^{\frac{W _{0} ( \frac{1}{2} )}{2}} - \frac{W _{0} ( \frac{1}{2} )}{2} - 2

Graph

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y^'=e^{(5x+4y)}

(dy)/(dx)=6x^2sqrt(y)

Frequently Asked Questions (FAQ)

What is the f(x)=e^x-sqrt(x)-2 ?
The f(x)=e^x-sqrt(x)-2 is