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Let f(x)={4x-x^3+log(a^2-3a+3),0 {x-18 >=3 Then the complete set of 'a' such that f(x)has local maxima at x=3

 
Let f(x)={4x-x^3+log(a^2-3a+3),0
                 {x-18 >=3
 Then the complete set of 'a' such that f(x)has local maxima at x=3

Grade:12th pass

2 Answers

Arun
25757 Points
3 years ago
Dear student
 
f’(x) = 4 – 3x^2
       = 1
 
f(3)
 
 – 15
 
a^2 – 3a + 3 >= 1
 
(a-1)(a-2) >= 0
 
a belongs to ( – infinity, 1) U (2, infinity)
Vikas TU
14149 Points
3 years ago
Dear student
F’(x) = 4x – 3x^2 +  \frac{1}{(a^2-3a+3)}
So , the value of x is x>= 15 
put x = 15 
for this t be local maximum 
The value of (a^2-3a+3) must be less than 0 
So , (a-1)(a-2) must be less than 0 
So , value of a must be (-inf , -1) U (1,2) 
Because there is log and value can not be between (-1 , 1) 
Hope this helps 
Good Luck 

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