Discussion Forum



1)

Let $f:D\rightarrow R,D\subseteq R, c \in D$  and r be a non zero real number . Consider the following statements:

I: c is  an extreme  point of f $\Rightarrow$ c is  an extreme point of rf

II. c is an extreme point of f $\Rightarrow$ c  is an extreme  point of r+f

Which of the following is correct?


A) Only (i) is true

B) Only (ii) is true

C) Both (i) and (ii) are true

D) Neither (i) nor(ii) is true

Answer:

Option C

Explanation:

I. Let the function 

            y= f(x)

c is extreme point of f 

 $\therefore$    f'(c)=0

 Now, y=r f'(x)

                               $\frac{dy}{dx}= r f'(x)$

 $\left(\frac{dy}{dx}\right)_{x=c}=rf'(c)$

   f'(c)=0

 $\therefore$ C is also extreme point  of rf.

II. Let               y=r+f(x)

            $\frac{dy}{dx}=f'(x)$

c is extreme  point of f(x).

 $\because$       $\left(\frac{dy}{dx}\right)_{x=c}=0$

$\Rightarrow$     c is also extreme point of r+f . Hence both statement are true.