Question

Complete the sentence below. A function f is​ _____ on an open interval I​ if, for any choice of x1 and x2 in​ I, with x1less than

Answer 1

Increasing if f' >0 and decreasing if f'<0

Explanation:

Difference quotient got by getting

`(f(x+h)-f(x))/(h)` will be greater than 0 if function is increasing otherwise negative

Here h is a small positive value.

In other words, we find that whenever first derivative of a function f(x) is positive the function is increasing.

Here given that for x1, x2 where x1<x2, we have

if f(x1) <f(x2) then the function is decreasing.

Or if x1<x2 and if f(x1) >f(x2) for all x1, and x2 in I the open interval we say f(x) is decreasing in I.