Answer :
Answer:
Increasing if f' >0 and decreasing if f'<0
Step-by-step explanation:
Difference quotient got by getting
[tex]\frac{f(x+h)-f(x)}{h}[/tex] 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.