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})

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

f (x, y) = x^{3} + 6 x y + 3 y^{2}

f (x, y) = x^{3} + 3 x y^{2} - 15 x + y^{3} - 15 y

f (x) = x^{\frac{1}{3}} (x + 4)

f (x) = 3 x^{4} - 4 x^{3} - 12 x^{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)