Prove that the following functions do not have maxima or minima:(i) `f (x) = e x` (ii) `g(x) = log x`(iii) `h(x)=x^3+x^2+x+1`

Explanation

(i) `f(x) = e^(x)`
` rArr f'(x) = e^(x) ne 0 forall x in R`
` :. ` f has no maximum or minimum value.
(ii) ` g(x) = log x`
` rArr g'(x) = 1/x ne 0 forall x in R`
`:.` g has no maximum or minimum value.
(iii) ` d(x) = x^(3)+x^(2)+x+1`
` rArr h'(x) = 3x^(2)+2x+1`
` = 3(x^(2)+2/3 x)+1`
` = 3(x^(2)+(2x)/3+1/9)+1-1/3`
`=3(x+1/3)^(2)+2/3 ne 0 forall x in R`
`:.` h(x) has no maximum or minimum value.