What is the extreme f(x)=e^x+x^2 ?

The extreme f(x)=e^x+x^2 is Minimum(-\W_{0}(1/2),e^{-\W_{0}(1/2)}+\W_{0}(1/2)^2)

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

extreme points

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

Minimum (- W_{0} (\frac{1}{2}), e^{- W_{0} (\frac{1}{2})} + W_{0} (\frac{1}{2})^{2})

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < - W_{0} (\frac{1}{2}),

Increasing

: - W_{0} (\frac{1}{2}) < x < \infty

Plug

x = - W_{0} (\frac{1}{2})

into

e^{x} + x^{2} : e^{- W_{0} (\frac{1}{2})} + W_{0} (\frac{1}{2})^{2}

Minimum (- W_{0} (\frac{1}{2}), e^{- W_{0} (\frac{1}{2})} + W_{0} (\frac{1}{2})^{2})

What is the extreme f(x)=e^x+x^2 ?
The extreme f(x)=e^x+x^2 is Minimum(-\W_{0}(1/2),e^{-\W_{0}(1/2)}+\W_{0}(1/2)^2)