Let `f(x)=|x-1|+|x-2| and g(x)={min{f(t):0 le t le x, 0 le x le 3 and x-2, x>3` then `g(x)` is not differentiable at

Let f(x) be defined on [-2,2[ such that f(x)={{:(,-1,-2 le x le 0),(,x-1,0 le x le 2):} and g(x)= f(|x|)+|f(x)| . Then g(x) is differentiable in the interval.

If f (x) = 4x ^(3) -x ^(2) -2x +1 and g (x) = {{:(min {f(t): 0 le t le x},, 0 le x le1),(3-x,, 1 lt x le 2):} and if lamda=g ((1)/(4))+g ((3)/(4))+g ((5)/(4)), then 2 lamda=

If f (x) = 4x ^(3) -x ^(2) -2x +1 and g (x) = {{:(min {f(t): 0 le t le x},, 0 le x le1),(3-x,, 1 lt x le 2):} and if lamda=g ((1)/(4))+g ((3)/(4))+g ((5)/(4)), then 2 lamda=

Let f(x) = -x^(3) + x^(2) - x + 1 and g(x) = {{:(min(f(t))",",0 le t le x and 0 le x le 1),(x - 1",",1 lt x le 2):} Then, the value of lim_(x rarr 1) g(g(x)) , is........ .

If f(x) = x^(2) - 2|x| and g(x) = {{:("min{f(t)":-2 le t le x",",-2 le x le "}"),("max {f(t):"0 le t le x",",0 le x le 3"}"):} (i) Draw the graph of f(x) and discuss its continuity and differentiablity. (ii) Find and draw the graph of g(x Also, discuss the continuity.

Let f(x) = 1 + 4x - x^(2), AA x in R g(x) = max {f(t), x le t le (x + 1), 0 le x lt 3} = min {(x + 3), 3 le x le 5} Verify conntinuity of g(x), for all x in [0, 5]