Question

Shorcut way to find increasing decreasing interval by simplify last interval

Answer 1

A function is called increasing if it increases as the input x moves from left to right, and is called decreasing if it decreases as x moves from left to right. Of course, a function can be increasing in some places and decreasing in others: that's the complication.

We can notice that a function is increasing if the slope of its tangent is positive, and decreasing if the slope of its tangent is negative. Continuing with the idea that the slope of the tangent is the derivative: a function is increasing where its derivative is positive, and is decreasing where its derivative is negative.