1.

Find the absolute maximum and the absolute minimum values of the following functions in the given intervals : f(x) = (x – 1)2 + 3 in [–3, 1]

Answer»

Given function is :

f(x) = (x – 1)2 + 3

∴f'(x) = 2(x – 1)

Now, 

f'(x) = 0 

2(x – 1) = 0 

x = 1 

Then, 

We evaluate of f at critical points x = 1 and at the interval [– 3, 1] 

f(1) = (1 – 1)2 + 3 = 3 

f(– 3) = (– 3 – 1)2 + 3 = 19 

Hence, 

We can conclude that the absolute maximum value of f on [ – 3, 1] is 19 occurring at x = – 3 and the minimum value of f on [ – 3, 1] is 3 occurring at x = 1



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