f(x) = max [2x+1, 3-4x]. Find min f(x)?

Download Inequalities formulas for CAT, which will covers various tips, shortcuts and concpets. 

Hi Navneet,

The point of intersection of y = 2x + 1 and y = 3 - 4x is at x = 1/3 and y = 5/3

For x < 1/3, 3-4x > 2x+1 => f(x) = 3-4x
For x >= 1/3, 2x+1 > 3-4x => f(x) = 2x+1

3-4x is a decreasing function from -infinity to x = 1/3 and 2x+1 is an increasing function from x = 1/3 to infinity.

So, the minimum value of f(x) is the point of intersection of both the graphs and it occurs at x = 1/3

The min. value of f(x) = f(1/3) = 5/3

Thanks Aaditya.

And how do we find the maximum value of the function? It should be infinity right?