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Question
If the derivative of the function f(x) is positive at a particular point, then about that point the value of the function is decreasing as the x-value increases.
If the derivative of the function f(x) is positive at a particular point, then about that point the value of the function is decreasing as the x-value increases.
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Solution
The correct option is B False
Look at the following curves carefully.
We know that the derivative at a point is nothing but the slope of tangent at that point which in itself is indicative of the steepness of the curve at that point. In curve (1) it is easy to observe that at every point (just like point A), the slope of the tangent (tan ɵ) should be positive and the curve , you can see is increasing as value of x-increases. But in curve (2)you can see that the tan ɵ (slope of tangent) is always negative (because ɵ here is always obtuse) and the curve is decreasing as the x-value increases.
Since tanθ = derivative of f(x). So if derivative is positive, then, y value increases as x – value increases.
So given statement is false
Look at the following curves carefully.
We know that the derivative at a point is nothing but the slope of tangent at that point which in itself is indicative of the steepness of the curve at that point. In curve (1) it is easy to observe that at every point (just like point A), the slope of the tangent (tan ɵ) should be positive and the curve , you can see is increasing as value of x-increases. But in curve (2)you can see that the tan ɵ (slope of tangent) is always negative (because ɵ here is always obtuse) and the curve is decreasing as the x-value increases.
Since tanθ = derivative of f(x). So if derivative is positive, then, y value increases as x – value increases.
So given statement is false
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