Question

For each real number x, f(x) is defined to be the smallest of the values of 2x + 3, 3x - 2 and 25 - x. What is the maximum value of f(x)?

Answer 1

9514 1404 393

Answer:

17 2/3

Explanation:

A calculator or spreadsheet can figure this. The maximum of f(x) is found where 3x-2 intersects 25-x.

2x +3 = 25 -x

3x = 22

x = 22/3 = 7 1/3

25 -7 1/3 = 17 2/3 . . . . maximum value of f(x)

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Note in the graph that the slope of f(x) decreases at about x=5. The expression with the lower positive slope is 2x+3. So, it is that expression that must equal the expression with the negative slope.