Find the maximum and minimum values, if any of the following function given by:
$f (x) = | sin 4 x + 3 |$

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Solution

$f (x) = | sin 4 x + 3 |$

We know that, $- 1 \leq sin θ \leq 1, \forall θ \in R$

Hence $f_{m a x} = | 1 + 3 | = 4$ and $f_{m i n} = | - 1 + 3 | = 2$

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Similar questions

Find the maximum and minimum values, if any, of the following function given by,

$f (x) = | s i n 4 x + 3 |$

f (x) = | x + 2 | - 1

g (x) = - | x + 1 | + 3

f (x) = | sin 4 x + 3 |

Find the maximum and minimum values, if any, of the following functions given by

(i) f(x) = |x + 2| − 1 (ii) g(x) = − |x + 1| + 3

(iii) h(x) = sin(2x) + 5 (iv) f(x) = |sin 4x + 3|

(v) h(x) = x + 1, x (−1, 1)

Find the maximum and minimum values, if any, of the following functions given by

$f (x) = | x + 2 | - 1$

$g (x) = - | x + 1 | + 3$

$h (x) = s i n (2 x) + 5$

$f (x) = | s i n 4 x + 3 |$

$h (x) = x + 1, x ϵ (- 1, 1)$

f (x) = {(2 x - 1)}^{2} + 3

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