Find the maximum and minimum value, f(x) = -(x - 1)2 + 10 - Vidyadip

Question

Find the maximum and minimum value, f(x) = -(x - 1)² + 10

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Answer

It is given that f(x) = -(x - 1)² + 10
Now, we can see that (x - 1)² $\ge$ 0 for every x $\in$ R
$\Rightarrow$ f(x) = -(x - 1)² + 10 $\le$ 10 for every x $\in$ R
The maximum value of f is attained when x - 1 = 0
i.e, x - 1 = 0
$\Rightarrow$ x = 1
Then, Maximum value of f = f(1) = -(1 - 1)² + 10 = 10
Since, x = 1 is the only critical point,
Therefore, function f does not have a minimum value.

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