Q .   F i n d   t h e   i n t e r v a l s   i n   w h i c h   t h e   f o l l o w i n g   f u n c t i o n s   a r e   a   i n c r e a sin g   b   d e c r e a sin g f x   =   2 x 3 - 15 x 2 + 36 x + 1

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  • -1
see the solution in given image
  • 0
y' = 6x2 - 30x + 36
    =6(x2 - 5x + 6)
    =6(x-3)(x-2)
for critical points, y' = 0
(x-3)(x-2) = 0
x = 2 or 3

these values of x divide number line into 3 segments, 
for inc. dec. we will check sign of y' in these intervals,
if it is positive, function is inc and if negative then it is dec.

so, f(x) is inc. in (-infinie,2) and (3,infinite)
and dec. in (2,3)
  • 0
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