Find the absolute maximum value and the absolute minimum value of… - Vidyadip

Question

Find the absolute maximum value and the absolute minimum value of the function:
$f(x)=(x-1)^{2}+3, x \in[-3,1]$

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Answer

Given that $f(x)=(x-1)^{2}+3, x \in[-3,1]$
$\Rightarrow$ f'(x) = 2(x - 1)
Now, f'(x) = 0
$\Rightarrow$ 2(x - 1) = 0
$\Rightarrow$ x = 1
Now, we evaluate the value of 'f ' at critical point x = 1, and at end points of the interval [-3, 1].
f(1) = (1 - 1)² + 3 = 0 + 3 = 3
f(-3) = (-3 - 1)² + 3 = 16 + 3 = 19
Therefore, the absolute maximum value of f on [-3, 1] is 19 occuring at x = -3.
And the absolute minimum value of f on [-3, 1] is 3 occurring at x = 1.

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