Single correct option
What is the minimum value of f(x) = max(2x + 1, 7 − x) over all real numbers x?
- A. 7
- B. 4
- C. 3
- D. 5
Show answer and solution
Answer: (D) 5
2x + 1 is increasing and 7 − x is decreasing. The maximum of an increasing and a decreasing line is smallest where they cross.
2x + 1 = 7 − x → x = 2, value = 5.
For x < 2 the max is 7 − x > 5; for x > 2 the max is 2x + 1 > 5. So the minimum is 5.
Tip: Sketching the 'V'-shaped upper envelope makes this instant.
2x + 1 = 7 − x → x = 2, value = 5.
For x < 2 the max is 7 − x > 5; for x > 2 the max is 2x + 1 > 5. So the minimum is 5.
Tip: Sketching the 'V'-shaped upper envelope makes this instant.
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