Mixing
Is it possible to visualise how graph of product of two functions look like?
$begingroup$
We can easily predict without calculating how a graph of sum of two functions will look like. And its helpful.
Is it possible to do with product?
functions graphing-functions
edited Feb 2 at 1:12
Misha Lavrov
49k757107
asked Feb 1 at 19:29
Abhishek DaberaoAbhishek Daberao
111
$endgroup$
add a comment |
$begingroup$
We can easily predict without calculating how a graph of sum of two functions will look like. And its helpful.
Is it possible to do with product?
functions graphing-functions
edited Feb 2 at 1:12
Misha Lavrov
49k757107
asked Feb 1 at 19:29
Abhishek DaberaoAbhishek Daberao
111
$endgroup$
$begingroup$
I'm not entirely convinced of the premise: just given the graphs of $sin(10x)$ and $sin(9x)$ would you easily be able to predict the shape of the graph of $sin(10x) + sin(9x)$?
$endgroup$
– Daniel Schepler
Feb 2 at 1:18
add a comment |
$begingroup$
We can easily predict without calculating how a graph of sum of two functions will look like. And its helpful.
Is it possible to do with product?
functions graphing-functions
edited Feb 2 at 1:12
Misha Lavrov
49k757107
asked Feb 1 at 19:29
Abhishek DaberaoAbhishek Daberao
111
$endgroup$
We can easily predict without calculating how a graph of sum of two functions will look like. And its helpful.
Is it possible to do with product?
functions graphing-functions
functions graphing-functions
edited Feb 2 at 1:12
Misha Lavrov
49k757107
asked Feb 1 at 19:29
Abhishek DaberaoAbhishek Daberao
111
edited Feb 2 at 1:12
Misha Lavrov
49k757107
asked Feb 1 at 19:29
Abhishek DaberaoAbhishek Daberao
111
edited Feb 2 at 1:12
Misha Lavrov
49k757107
edited Feb 2 at 1:12
Misha Lavrov
49k757107
edited Feb 2 at 1:12
Misha Lavrov
49k757107
49k757107
asked Feb 1 at 19:29
Abhishek DaberaoAbhishek Daberao
111
asked Feb 1 at 19:29
Abhishek DaberaoAbhishek Daberao
111
asked Feb 1 at 19:29
Abhishek DaberaoAbhishek Daberao
111
111
$begingroup$
I'm not entirely convinced of the premise: just given the graphs of $sin(10x)$ and $sin(9x)$ would you easily be able to predict the shape of the graph of $sin(10x) + sin(9x)$?
$endgroup$
– Daniel Schepler
Feb 2 at 1:18
add a comment |
$begingroup$
I'm not entirely convinced of the premise: just given the graphs of $sin(10x)$ and $sin(9x)$ would you easily be able to predict the shape of the graph of $sin(10x) + sin(9x)$?
$endgroup$
– Daniel Schepler
Feb 2 at 1:18
$begingroup$
I'm not entirely convinced of the premise: just given the graphs of $sin(10x)$ and $sin(9x)$ would you easily be able to predict the shape of the graph of $sin(10x) + sin(9x)$?
$endgroup$
– Daniel Schepler
Feb 2 at 1:18
$begingroup$
I'm not entirely convinced of the premise: just given the graphs of $sin(10x)$ and $sin(9x)$ would you easily be able to predict the shape of the graph of $sin(10x) + sin(9x)$?
$endgroup$
– Daniel Schepler
Feb 2 at 1:18
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
You know that it both functions are positive or both are negative at a point then their product will be positive. Otherwise the product will be negative. You also know that if either function is 0 at a point then the product will be (and that in fact these are the only places the product will be 0). Otherwise, if you haven't taken a calculus course there probably isn't a lot to easily find what the shape will look like except arguments like if the absolute value of one function is less than $1$ it will "shrink" the other function and otherwise it will "expand" it.
This is something I wondered often as a kid and didn't get a very good answer until I took a calculus course. After you've taken calculus, assuming the function behaves very nicely everywhere, the derivatives will tell you the type of information you're looking for.
answered Feb 1 at 20:55
Jon HilleryJon Hillery
707
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
You know that it both functions are positive or both are negative at a point then their product will be positive. Otherwise the product will be negative. You also know that if either function is 0 at a point then the product will be (and that in fact these are the only places the product will be 0). Otherwise, if you haven't taken a calculus course there probably isn't a lot to easily find what the shape will look like except arguments like if the absolute value of one function is less than $1$ it will "shrink" the other function and otherwise it will "expand" it.
This is something I wondered often as a kid and didn't get a very good answer until I took a calculus course. After you've taken calculus, assuming the function behaves very nicely everywhere, the derivatives will tell you the type of information you're looking for.
answered Feb 1 at 20:55
Jon HilleryJon Hillery
707
$endgroup$
add a comment |
$begingroup$
You know that it both functions are positive or both are negative at a point then their product will be positive. Otherwise the product will be negative. You also know that if either function is 0 at a point then the product will be (and that in fact these are the only places the product will be 0). Otherwise, if you haven't taken a calculus course there probably isn't a lot to easily find what the shape will look like except arguments like if the absolute value of one function is less than $1$ it will "shrink" the other function and otherwise it will "expand" it.
This is something I wondered often as a kid and didn't get a very good answer until I took a calculus course. After you've taken calculus, assuming the function behaves very nicely everywhere, the derivatives will tell you the type of information you're looking for.
answered Feb 1 at 20:55
Jon HilleryJon Hillery
707
$endgroup$
add a comment |
$begingroup$
You know that it both functions are positive or both are negative at a point then their product will be positive. Otherwise the product will be negative. You also know that if either function is 0 at a point then the product will be (and that in fact these are the only places the product will be 0). Otherwise, if you haven't taken a calculus course there probably isn't a lot to easily find what the shape will look like except arguments like if the absolute value of one function is less than $1$ it will "shrink" the other function and otherwise it will "expand" it.
This is something I wondered often as a kid and didn't get a very good answer until I took a calculus course. After you've taken calculus, assuming the function behaves very nicely everywhere, the derivatives will tell you the type of information you're looking for.
answered Feb 1 at 20:55
Jon HilleryJon Hillery
707
$endgroup$
You know that it both functions are positive or both are negative at a point then their product will be positive. Otherwise the product will be negative. You also know that if either function is 0 at a point then the product will be (and that in fact these are the only places the product will be 0). Otherwise, if you haven't taken a calculus course there probably isn't a lot to easily find what the shape will look like except arguments like if the absolute value of one function is less than $1$ it will "shrink" the other function and otherwise it will "expand" it.
This is something I wondered often as a kid and didn't get a very good answer until I took a calculus course. After you've taken calculus, assuming the function behaves very nicely everywhere, the derivatives will tell you the type of information you're looking for.
answered Feb 1 at 20:55
Jon HilleryJon Hillery
707
answered Feb 1 at 20:55
Jon HilleryJon Hillery
707
answered Feb 1 at 20:55
Jon HilleryJon Hillery
707
answered Feb 1 at 20:55
Jon HilleryJon Hillery
707
707
add a comment |
add a comment |
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$begingroup$
I'm not entirely convinced of the premise: just given the graphs of $sin(10x)$ and $sin(9x)$ would you easily be able to predict the shape of the graph of $sin(10x) + sin(9x)$?
$endgroup$
– Daniel Schepler
Feb 2 at 1:18