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

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

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

Thanks Aaditya.

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