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Convexity

The maximum v...

Question

The maximum value of the function $f (x) = | x - 4 |$ exists at

x = 0

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x = 2

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x = 4

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x = - 4

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Solution

The correct option is B $x = - 4$
There is no maximum value for this function, as the value keeps on increasing if we either go to left or right of $x = 4$ .
The farther away we go from $x = 4$ , the more the value of the function.
From the given options the maximum value is at $x = - 4$
Hence, D is correct.

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Similar questions

f (x) = [x] - [\frac{x}{4}], x \in R

[x]

f (x) = \frac{tan (\frac{π}{4} - x)}{cot 2 x}, (x \neq π / 4)

f (x)

x = π / 4

f (x)

[0, π / 2]

a

b

f (x) = a {tan}^{- 1} (\frac{1}{x - 4})

0 \leq x < 4;

f (x) = b {tan}^{- 1} (\frac{2}{x - 4})

4 < x < 6

f (4) = \frac{π}{2}

f (x) = {sin}^{- 1} (7 - x) + \frac{c x}{4}

6 \leq x \leq 8

[0, 8]

f (x) = \frac{tan (\frac{π}{4} - x)}{cot 2 x}

x \neq \frac{π}{4},

f (x)

x = \frac{π}{4}

f (x)

[0, π / 2]

f (0)

f (x) = \frac{2 - \sqrt{(x + 4)}}{sin 2 x}, x \neq 0

x = 0

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