# Change of signs

 Enter your function here. Hint: Enter as 3*x^2 , as 3/5 and as (x+1)/(x-2x^4)

## What is the use of the change of sign?

By checking for the change of sign, you can check whether a function with derivative has a maximum / minimum turning point or a saddle point. Here are three examples where the function has slope in (1|2):

This function has slope in (1|2) and a maximum turning point. At the graph ascends, i.e. the derivative is larger than in here. At the Graph falls, i.e. the derivative is less than . This means that around a maximum turning point, the sign of the derivative is + before and - after the turning point. This means the derivative changes signs from + to - .

This function has slope in (1|2), but a minimum turning point. At the graph falls, i.e. the derivation here is less than . At the graph ascends, i.e. the derivation is larger than . This implies that at a minimum turning point, the sign of the derivation is - before and + after the turning point. This means the derivation changes signes from - to +.

This function also has slope at (1|2), but no turning point. You see that the graph ascends at as well as at . This implies you have no turning point if the derivation does not change signs. Such a point (that is no turning point but has derivation ) is called saddle point.