Show that none of the following functions has a local maximum or a local minimum: `x^3+x^2+x+1` (ii) `e^x`

Explanation

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


` f^{prime}(x) =3 x^{2}+2 x+1 `


`=3(x^{2}+2 / 3 x+1 / 3) `


`=3((x+1 / 3)^{2}-1 / y+1 / 3) `


` =3((x+1 / 3)^{2}+2 / y) `



`f^{prime}(x)=underbrace{3(x+1 / 3)^{2}}_{>0}+underbrace{2 / 3}_{>0}`



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