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Question

If f(x) = min (7x + 3, 8x – 6) for 0< x < 4, then determine the maximum value of f(x).
  1. 31
  2. 66
  3. 28
  4. 26


Solution

The correct option is D 26

Equate the two terms to get the point of intersection

7x+3=8x-6

X=9, which is greater than the given constraint

Minimum/Maximum of two increasing function will also be an increasing function.

Here 7x + 3 and 8x – 6 are both increasing functions, so f(x) will also be an increasing function.

Based on the constraints given, max of f(x) will occur at x = 4 i.e. f(4) = min (31, 26) = 26

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