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?
2026-04-01 11:22:47.1775042567
Is it possible to visualise how graph of product of two functions look like?
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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.