Homework SourseSuppose the derivative of a function f is as given below Sta
Suppose the derivative of a function f is as given below. State the largest open interval on which f is increasing.
f \'(x) = (x + 1)2(x 2)3(x 4)4
Solution
given f \'(x) = (x + 1)2(x 2)3(x 4)4
when f is increasing ,f \'(x)>0
=> (x + 1)2(x 2)3(x 4)4>0
=>x+10,x-40 ,(x-2)3>0.................... since (x + 1)2(x 4)4 is always non-negative
=>x-1, x4 , x>2
f is increasing is (2,4)U(4,)
at x =4 , f is neither increasing nor decresing
