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junior college 1 | H1 Maths
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why ans is A？
Date Posted: 3 years ago
Views: 390
This question requires the pre-requisite idea from trigonometry that -1 ≤ sin x ≤ 1 for all real values of x.
Does this ring a bell to you?
Think again. Where did you see the relation -1 ≤ sin x ≤ 1?
From here, we can deduce, by adding the number 2 to all three sides of the inequality, that 1 ≤ 2 + sin x ≤ 3, so this results in 1 ≤ dy/dx ≤ 3.
This means that the values of dy/dx can range from 1 to 3 (inclusive of the two boundary values). In any case, this range (of 1 to 3) already exceeds 0, so we can safely say that dy/dx > 0 whatever the case is.
Since dy/dx > 0 at all times, this indicates that the gradient of the graph is always positive, so the curve is always increasing,
Does this ring a bell to you?
Think again. Where did you see the relation -1 ≤ sin x ≤ 1?
From here, we can deduce, by adding the number 2 to all three sides of the inequality, that 1 ≤ 2 + sin x ≤ 3, so this results in 1 ≤ dy/dx ≤ 3.
This means that the values of dy/dx can range from 1 to 3 (inclusive of the two boundary values). In any case, this range (of 1 to 3) already exceeds 0, so we can safely say that dy/dx > 0 whatever the case is.
Since dy/dx > 0 at all times, this indicates that the gradient of the graph is always positive, so the curve is always increasing,
See 1 Answer
hii how to see the gradient is positive？？
dy/dx is the gradiend G from the graph I added in, dy/dx is always between1 and 3 (inclusive). So it is always greater than or equal to 1... That is always positive
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