Question

Which of the following functions does not have a maximum or minimum?

• A. $15-(x-1{)}^{15}$
• B. $x^5+3x^4+2$
• C. $x^7+x^5+2x^3+2$
• D. $(x-5{)}^{16}$

Answer 1

Answer: (A), (C)

The correct options are
A $15-(x-1{)}^{15}$
C $x^7+x^5+2x^3+2$

Since all the term in $f\left(x\right)=x^7+x^5+2x^3+2$ contain odd powers with a+ sign all the terms in $f^{\prime }\left(x\right),i^m\left(x\right)$ in any odd differential coefficient are positive with even power of x .
$\therefore$ any odd differential coefficient of f(x) cannot be zero.
$15-(x-1{)}^{15}$ is a decreasing function .