Home
Class 12
MATHS
If f(x) = x^(2) - 2|x| and g(x) = {{:("m...

If `f(x) = x^(2) - 2|x| and g(x) = {{:("min{f(t)":-2 le t le x",",-2 le x le 0 "}"),("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.

Text Solution

Verified by Experts

The correct Answer is:
x = 0
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x) = {|x|-|x-1|}^(2) , draw the graph of f(x) and discuss its continuity and differentiability of f(x)

Let f(x) = x^(3) - x^(2) + x + 1 and g(x) = {{:(max f(t)",", 0 le t le x,"for",0 le x le 1),(3-x",",1 lt x le 2,,):} Then, g(x) in [0, 2] is

f(x) = {(3",","if" 0 le x le 1),(4",","if" 1 lt x lt 3),(5",","if" 3 le x le 10):}

Let f(x) = x^(4) - 8x^(3) + 22x^(2) - 24x and g(x) = {{:(min f(x)",",x le t le x + 1 -1 le x le 1),(x - 10",",x ge 1):} Discuss the continuity and differentiability of g(x) in [-1, oo)

f(x)= {(|x+1|",",x lt -2),(2x+3",",-2 le x lt 0),(x^(2) + 3",",0 le x lt 3),(x^(3)-15,3 le x):} . Find at which points, the function f(x) is discontinuous ?

f(x)= {(2x",","if" x lt 0),(0",","if" 0 le x le 1),(4x",","if" x gt 1):}

Draw the graph of the function f(x) = x - |x - x^(2)|, -1 le x le 1 and discuss the continuity or discontinuity of f in the interval -1 le x le 1

f(x)= {(-2",","if" x le -1),(2x",","if" -1 lt x le 1),(2",","if " x gt 1):}