In Exercises 31 and 32 , locate the absolute extrema of the function (if any exist) over each interval. $f(x)=2x-3$(a) [0,2](b) [0,2)(c) (0,2](d) (0,2)

Step by Step Solution: Step 1. Differentiate the given function to find the critical points. Step 2. Find the critical points lying inside the given interval. Step 3. Find the value of function at these critical points as well as at end-points. Step 4. The minimum value is the least value, and the maximum value is the greatest value among all values obtained in the previous step. Final Answer: a. Absolute minimum is f(0) = -3; Absolute maximum is f(2) = 1\nb. Absolute minimum is f(0) = -3; Absolute maximum does not exist\nc. Absolute minimum does not exist; Absolute maximum is f(2) = 1\nd. Absolute minimum does not exist; Absolute maximum does not exist