Question

determinar ceros,máximos y mínimos
$f(x) \: = 3 \cos(x + \binom{\pi}{4} )$
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Answer 1

Respuesta:

1. Ceros: x = π/4 ± kπ (k = 0, 1, 2, ...)

2. Máximos: x = -π/4 ± 2kπ (k = 0, 1, 2, ...)

3. Mínimos:  x = 3π/4 ± 2kπ (k = 0, 1, 2, ...)

Explicación paso a paso:

1. Ceros

3cos(x + π/4) = 0

x + π/4 = π/2 ± kπ (k = 0, 1, 2, ...)

x = π/2 - π/4 ± kπ (k = 0, 1, 2, ...)

x = π/4 ± kπ (k = 0, 1, 2, ...)

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2. Máximos

3cos(x + π/4) = 3

x + π/4 = ± 2kπ (k = 0, 1, 2, ...)

x = -π/4 ± 2kπ (k = 0, 1, 2, ...)

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3. Mínimos

3cos(x + π/4) = -3

x + π/4 = π ± 2kπ (k = 0, 1, 2, ...)

x = π -π/4 ± 2kπ (k = 0, 1, 2, ...)

x = 3π/4 ± 2kπ (k = 0, 1, 2, ...)