Hi you all
I have a quick and properly really easy question.
I saw around the internet that the minimum function can be written out:
I haven't ever seen that before, so i am interested in knowing when it works and when it doesn't (and to some extent why it's true). I need to differentiate a minimum function in my exam in microeconomics so it would be a great help!
Best regards.
if you have
a(x) = min(b(x),c(x))
Except in special cases, The function will not normally be differenciable at the point b(x) = c(x). it will be differenciable at other points provided b(x) and c(x) are differenciable.
What is the economics problem you are trying to solve? It may be easier to assume min(a,b) = a; and check that your solution is at a point . If that doesn't work then assume min(a,b) = b and check that your solution is at a point .
I needed to differentiate a function with respect to two different variables and find the quotient of them in order to get a function which hopefully could tell me more about the function which i originally was assigned to find.
Even though it my problem seemed far fetched your hint of dividing into different situations actually worked like a charm. Thank you!