Question

Identify the correct statements
(a) Every constant function is an increasing function.
(b) Every constant function is a decreasing function.
(c) Every identify function is an increasing function.
(d) Every identify function is a decreasing function.

• A. $\left(a\right),\left(b\right)$ and $\left(c\right)$
• B. $\left(a\right)$ and $\left(c\right)$
• C. $\left(c\right)$ and $\left(d\right)$
• D. $\left(a\right),\left(c\right)$ and $\left(d\right)$

Answer 1

Answer: (A)

$\left(a\right),\left(b\right)$ and $\left(c\right)$

Increasing function means $f^{\prime }\left(x\right)\ge 0$ and decreasing function means $f^{\prime }\left(x\right)\le 0$

For constant function , derivative will be zero.

Therefore constant function is both increasing and decreasing.

Identity function means $f\left(x\right)=x$ , its derivative is always $1\ge 0$

Therefore identity function is increasing function

So $a,b,c$ are correct

Therefore the correct option is $A$