Extremal value problems - easy

Solution:
The minimal value could be in both ends of the interval or in a point, in which there is a local minimum for the function. We calculate and , which is obviously not the minimal value.
All that is left is to find the local extrema of the function. , so there are extrema in and . , so it is not a minimal value. . So the minimal value is and is reached in two points - and .

Solution:
Since f(x) is a linear function whose slope is 1, a positive number, it is strictly increasing for all x. Therefore its maximal value is reached for the largest value of x, x=13 and f(x)=13-5=8.

Solution:
It is known that . We multiply this by 4 and get , so the maximal value for this function is 4.

Solution:
, we add -1 to both sides of the inequality and get .