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Global Maxima

Calculate the...

Question

Calculate the maximum value of $f (x) = 3 - (x + 2)^{2}$ .

- 3

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3

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5

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Solution

The correct option is E $3$
$f (x) = 3 - {(x + 2)}^{2}$ , for $f (x)$ to be maximum ${(x + 2)}^{2}$ should be minimum.
The minimum value of ${(x + 2)}^{2}$ is $0$ and occurs at $x = - 2$ .
Therefore the maximum value of $f (x)$ occurs at $x = - 2$ and the value is $3$ .

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Statement 1:

(\sqrt{- 3 + 4 x - x^{2}} + 4)^{2} + (x - 5)^{2}

1 \leq x \leq 3)

36.

Statement 2:

(5, - 4)

(x - 2)^{2} + y^{2} = 1

6

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