Answer:
1) increasing on (-∞,-1] ∪ [1,∞), decreasing on [-1,0) ∪ (0,1]
is local maximum,
is local minimum
2) increasing on [1,∞), decreasing on (-∞,0) ∪ (0,1]
is absolute minimum
3) increasing on (-∞,0] ∪ [8,∞), decreasing on [0,4) ∪ (4,8]
is local maximum,
is local minimum
4) increasing on [2,∞), decreasing on (-∞,2]
is absolute minimum
5) increasing on the interval (0,4/9], decreasing on the interval [4/9,∞)
is local minimum,
is absolute maximum
Step-by-step explanation:
To find minima and maxima the of the function, we must take the derivative and equalize it to zero to find the roots.
1) 
and 
So, the roots are
and 
The function is increasing on the interval (-∞,-1] ∪ [1,∞)
The function is decreasing on the interval [-1,0) ∪ (0,1]
is local maximum,
is local minimum.
2) 
and 
So the root is 
The function is increasing on the interval [1,∞)
The function is decreasing on the interval (-∞,0) ∪ (0,1]
is absolute minimum.
3) 
and 
So the roots are
and 
The function is increasing on the interval (-∞,0] ∪ [8,∞)
The function is decreasing on the interval [0,4) ∪ (4,8]
is local maximum,
is local minimum.
4) 
has no solution and
is crtitical point.
The function is increasing on the interval [2,∞)
The function is decreasing on the interval (-∞,2]
is absolute minimum.
5)
for 

So the root is 
The function is increasing on the interval (0,4/9]
The function is decreasing on the interval [4/9,∞)
is local minimum,
is absolute maximum.