Question

What is the maximum value of the function f(x) = min (7 - 9x, 3x + 4) for 0 < x < 9?

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is C

7- 9x is a decreasing function, while 3x +4 is an increasing function. The max of f(x) occurs
at the intersection of 7 - 9x and 3x + 4.
7- 9x = 3x + 4 $\to$ x = $\frac{1}{4}$
So, max f(x) = min $(\frac{19}{4},\frac{19}{4})$ = $\frac{19}{4}$