Answer:
(a) The critical points of f are x=0 and x=3.
(b)f is decreasing on and f is decreasing on
.
(c) Therefore the local minimum of f is at x=3
Step-by-step explanation:
Given function is
(a)
To find the critical point set f'(x)=0
The critical points of f are 0,3.
(b)
The interval are and
.
To find the increasing or decreasing, taking two points one point from the interval (0,3) and another point .
Assume 1 and 4.
Now
and
Since 1∈ , f'(x)<0 and 4∈
, f'(x)>0
∴f is decreasing on and f is decreasing on
.
(c)
Differentiating with respect to x
Now
and
Since f''(x)>0 at x=3
Therefore the local minimum of f is at x=3