Find the maximum or minimum values ,if any without derivaties of the functions 1.sin 2x+5 and 2.|x+4|+6
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1. y = sin2x + 5
we know,
sin∅ always lies between -1 to 1
so,. -1 ≤ sin2x ≤ 1
add 5 in all sides,
-1 + 5 ≤ sin2x + 5 ≤ 1 + 5
4 ≤ sin2x + 5 ≤ 6
hence, maximum value of y= sin2x + 5 is 6 and minimum value is 4 .
means Range € [ 4, 6 ]
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2. y = | x + 4 | + 6
you can understand by seeing its graph.
maximum value of y is ∞ and minimum value is 6. means Range € [ 6, ∞)
we know,
sin∅ always lies between -1 to 1
so,. -1 ≤ sin2x ≤ 1
add 5 in all sides,
-1 + 5 ≤ sin2x + 5 ≤ 1 + 5
4 ≤ sin2x + 5 ≤ 6
hence, maximum value of y= sin2x + 5 is 6 and minimum value is 4 .
means Range € [ 4, 6 ]
================================
2. y = | x + 4 | + 6
you can understand by seeing its graph.
maximum value of y is ∞ and minimum value is 6. means Range € [ 6, ∞)
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