4) Prove that the following functions do not have maxima or minima:
 

(iii) h(x) = x^3 + x^2 + x +1


 

Answers (1)

Given function is 
h(x) = x^3 + x^2 + x +1
h^{'}(x) = 3x^2+2x+1\\ h^{'}(x) = 0\\ 3x^2+2x+1 = 0\\ 2x^2+x^2+2x+1 = 0\\ 2x^2 + (x+1)^2 = 0\\
But, it is clear that there is no c \ \epsilon \ R such that f^{'}(c) = 0
Hence, the function h(x) = x^3 + x^2 + x +1 does not have  either maxima or minima

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