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  • Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: f (x) = (x −1)^2 + 3

5.Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:

(iv) f (x) = ( x-1) ^2 + 3 , x \epsilon [ -3 , 1 ]

Answers (1)

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Given function is 
f(x) = (x-1)^2+3
f^{'}(x) =2(x-1) \\ f^{'}(x)= 0\\ 2(x-1)= 0\\ x=1         
Hence, x = 1 is the critical point  of function f(x) = (x-1)^2+3
Now, we need to check the value of function f(x) = (x-1)^2+3  at  x = 1  and at the end points of given range  i.e. at x = -3 and x =  1
f(1) = (1-1)^2+3 = 0^2+3 = 3
            
f(-3) = (-3-1)^2+3= (-4)^2+3 = 16+3= 19
f(1) = (1-1)^2+3 = 0^2+3 = 3
Hence,  absolute maximum value of function  f(x) = (x-1)^2+3  occurs at x = -3 and value is 19
and absolute minimum value of function f(x) = (x-1)^2+3  occurs at x = 1 and value is 3

Posted by

Gautam harsolia

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