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Popular >

f(x)=2^x+x^2

Solution

f (x) = 2^{x} + x^{2}

Solution

Domain : - \infty < x < \infty

Range : f (x) \geq 2^{- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{l n ( 2 )}} + \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} ) ^{2}}{ln ^{2} ( 2 )}

Y Intercepts : (0, 1)

Asymptotes : None

Extreme Points : Minimum - \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{ln ( 2 )}, 2^{- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{l n ( 2 )}} + \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} ) ^{2}}{ln ^{2} ( 2 )}

+1

Interval Notation

Domain : (- \infty, \infty)

Range : 2^{- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{l n ( 2 )}} + \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} ) ^{2}}{ln ^{2} ( 2 )}, \infty

Solution steps

Domain of

2^{x} + x^{2} : - \infty < x < \infty

Range of

2^{x} + x^{2} : f (x) \geq 2^{- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{l n ( 2 )}} + \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} ) ^{2}}{ln ^{2} ( 2 )}

Axis interception points of

2^{x} + x^{2} :

Y Intercepts

: (0, 1)

Asymptotes of

2^{x} + x^{2} :

None

Extreme Points of

2^{x} + x^{2} :

Minimum

- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{ln ( 2 )}, 2^{- \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} )}{l n ( 2 )}} + \frac{W _{0} ( \frac{l n ^{2} ( 2 )}{2} ) ^{2}}{ln ^{2} ( 2 )}

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