What does it mean for a function to be semi-monotonic?
up vote
0
down vote
favorite
I mostly understand monotonic functions as described by wikipedia. However, I do not understand what it means for a function to be semi-monotonic as described in the java math class. This page helped a little bit but I still don't understand it. The list below is the best that I can explain what I'm trying to figure out since I don't know what I don't know.
- Does monotonicity apply only to the signs' of the mathematical function's and its corresponding approximation's first derivative or does it make sense to say that the monotonicity of $sin(fracpi4)$ is $frac{sqrt2}{2}$ since the value of its first derivative at $fracpi4$ is $frac{sqrt2}{2}$?
- How can you prove that an approximation of a differentiable function is semi-monotonic?
- Can you think of an approximation of sine or any other differentiable function that closely represents the actual function, but the derivative of that approximation does not represent the derivative of the actual function's derivative?
functions trigonometry approximation monotone-functions
asked Nov 15 at 5:19
Deoxal
84
add a comment |
up vote
0
down vote
favorite
I mostly understand monotonic functions as described by wikipedia. However, I do not understand what it means for a function to be semi-monotonic as described in the java math class. This page helped a little bit but I still don't understand it. The list below is the best that I can explain what I'm trying to figure out since I don't know what I don't know.
- Does monotonicity apply only to the signs' of the mathematical function's and its corresponding approximation's first derivative or does it make sense to say that the monotonicity of $sin(fracpi4)$ is $frac{sqrt2}{2}$ since the value of its first derivative at $fracpi4$ is $frac{sqrt2}{2}$?
- How can you prove that an approximation of a differentiable function is semi-monotonic?
- Can you think of an approximation of sine or any other differentiable function that closely represents the actual function, but the derivative of that approximation does not represent the derivative of the actual function's derivative?
functions trigonometry approximation monotone-functions
asked Nov 15 at 5:19
Deoxal
84
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I mostly understand monotonic functions as described by wikipedia. However, I do not understand what it means for a function to be semi-monotonic as described in the java math class. This page helped a little bit but I still don't understand it. The list below is the best that I can explain what I'm trying to figure out since I don't know what I don't know.
- Does monotonicity apply only to the signs' of the mathematical function's and its corresponding approximation's first derivative or does it make sense to say that the monotonicity of $sin(fracpi4)$ is $frac{sqrt2}{2}$ since the value of its first derivative at $fracpi4$ is $frac{sqrt2}{2}$?
- How can you prove that an approximation of a differentiable function is semi-monotonic?
- Can you think of an approximation of sine or any other differentiable function that closely represents the actual function, but the derivative of that approximation does not represent the derivative of the actual function's derivative?
functions trigonometry approximation monotone-functions
asked Nov 15 at 5:19
Deoxal
84
I mostly understand monotonic functions as described by wikipedia. However, I do not understand what it means for a function to be semi-monotonic as described in the java math class. This page helped a little bit but I still don't understand it. The list below is the best that I can explain what I'm trying to figure out since I don't know what I don't know.
- Does monotonicity apply only to the signs' of the mathematical function's and its corresponding approximation's first derivative or does it make sense to say that the monotonicity of $sin(fracpi4)$ is $frac{sqrt2}{2}$ since the value of its first derivative at $fracpi4$ is $frac{sqrt2}{2}$?
- How can you prove that an approximation of a differentiable function is semi-monotonic?
- Can you think of an approximation of sine or any other differentiable function that closely represents the actual function, but the derivative of that approximation does not represent the derivative of the actual function's derivative?
functions trigonometry approximation monotone-functions
functions trigonometry approximation monotone-functions
asked Nov 15 at 5:19
Deoxal
84
asked Nov 15 at 5:19
Deoxal
84
asked Nov 15 at 5:19
Deoxal
84
asked Nov 15 at 5:19
Deoxal
84
asked Nov 15 at 5:19
Deoxal
84
84
add a comment |
add a comment |
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
active
oldest
votes
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2999255%2fwhat-does-it-mean-for-a-function-to-be-semi-monotonic%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
