Find the local extrema of $f$. (Extrema just means either a maximum or a minimum.) For each extremum calculate three things: the location of the extremum (i.e., value of $x$), the value of the extremum (i.e., value of $f(x)$), and whether it is a local maximum or a local minimum.
Locations of the local extrema:
(If multiple answers, enter in increasing order, separated by commas; if no answers, enter none.)
Values of the local extrema:
(If multiple answers, enter in the same order as above, separated by commas; if no answers, enter none. If rounding, keep at least four digits.)
For each extremum, enter either maximum or minimum to indicate if the extremum is a local maximum or local minimum, respectively. (If multiple answers, enter in the same order as above, separated by commas; if no answers, enter none.)
Characterization of extrema=
Hint
For example, imagine that there were local extrema at $x=-4$, $x=-1$, and $x=3$. Imagine moreover, that $f(-4)=0$, $f(-1)=-3$, and $f(3)=4$, and that these extrema were a local maximum, a local minimum, and a local maximum, respectively. Then, the correct answer would be to enter
-4,-1, 3 in the locations blank, enter
0, -3, 4 in the values blank, and
maximum, minimum, maximum in the characterization blank.
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Find the global maximum and global minimum of the function $f(x)$ on the interval $1 \le x \le 6$. Also indicate the location (the value of $x$) of the global maximum and global minimum.
Global maximum:
(If rounding, keep at least four digits.)
Location of global maximum: $x =$
Global minimum:
(If rounding, keep at least four digits.)
Location of global minimum: $x= $