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RicardoOOO
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Consider the function f(x) = ln (cos^2(x)) When is it increasing/decreasing?
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If the derivative f'(x) is positive, what does that tell you about f(x)? What about when f'(x) = 0? When f'(x) < 0?RicardoOOO said:Consider the function f(x) = ln (cos^2(x)) When is it increasing/decreasing?
That seems like it would be the answer for a simpler function, but I would find it easier here to just examine the function itself.SteamKing said:If the derivative f'(x) is positive, what does that tell you about f(x)? What about when f'(x) = 0? When f'(x) < 0?
Merlin3189 said:That seems like it would be the answer for a simpler function, but I would find it easier here to just examine the function itself.
If OP is "new to calculus", will he be able to differentiate ln()? (I had to look it up - I'm too old to calculus!)
I had actually jumped to the assumption that OP might be differentiating a function to find turning points, then looking at the shape of the function (where increasing/decreasing) to decide what sort of turning points they were.
Just thought it worth mentioning that I'm not talking about "plotting" - just sketching and no real calculation beyond thinking, "log(1) is 0, so log(smaller than 1) is negative" and "squaring numbers 0 to |1| gives positive numbers 0 to 1, mainly a bit smaller".SteamKing said:Certainly, one can plot the function ...
.. the examination of the derivative can determine this without the tedious calculation of functional values.
When a function is increasing, it means that as the input values increase, the output values also increase. In other words, the graph of the function has a positive slope.
To determine if a trigonometric function is increasing or decreasing, you can take the derivative of the function and set it equal to zero. If the derivative is positive, the function is increasing, and if it is negative, the function is decreasing.
No, a trigonometric function can only be either increasing or decreasing at a given point. However, it is possible for a function to have both increasing and decreasing intervals.
To find the intervals on which a trigonometric function is increasing or decreasing, you can use the first or second derivative test. The first derivative test involves finding the critical points and evaluating the derivative at those points. The second derivative test involves finding the second derivative and determining its sign at the critical points.
Yes, when dealing with trigonometric functions, it is important to keep in mind that the domain may be limited and that the functions are periodic. This means that the functions repeat themselves every certain interval, which can affect the increasing or decreasing behavior of the function.