Applications Of Derivatives Question 59
Question: If sum of two numbers is 3, then maximum value of the product of first and the square of second is
[MP PET 1996]
Options:
A) 4
B) 3
C) 2
D) 1
Show Answer
Answer:
Correct Answer: A
Solution:
Let the first number be $ 3-x $ , then second will be $ x $ . Accordingly, we have to maximize $ (3-x)x^{2} $ Let $ f(x)=(3-x)x^{2}=3x^{2}-x^{3}\Rightarrow f’(x)=6x-3x^{2} $
$ \therefore f’(x)=0\Rightarrow x=0,\ 2 $ Also $ {f}’’,(x)=6-6x $ . Obviously, $ {f}’’,(2)=-6<0 $ . Therefore, required max. value $ =(3-2).,2^{2}=4. $
BETA
