f(x)=5x-4 `(0ltxle1) =4x^2-3x (1ltxlt2)` test whether f(x) is differentiable at x=1

Let f(x)={(x exp[-(1/|x|+1/x)], x ne 0),(0, x=0):} Test whether f(x) is differentiable at x=0

Let {:(f(x)=5x-4," ""when "0ltxle1),(=4x^(2)-3x," ""when "xgt1):} Discuss the differentiability of f(x) at x = 1 .

f(x)={{:(5x-4,"when "0ltxle1),(4x^(2)-3x,"when "xgt1):} Discuss the continuity and differentiability of f(x)"at" x =1

f(x) = {(|x+1|/(x+1),when x!= -1),(0, when x = -1):} Test whether f(x) is continuous or not at x= -1

Consider two functions y=f(x) and y=g(x) defined as f(x)= {[a x^2 +b, 0lexle1],[ bx + 2b, 1ltxle3],[(a-1)x + 2c - 3 , 3ltxle4]} And g(x)={[c x + d , 0le x le 2],[a x+3-c ,2ltxlt3],[x^2+b+1,3lexle4]} Let f be differentiable at x=1a n dg(x) be continuous at x=3. If the roots of the quadratic equation x^2+(a+b+c)alphax+49(k+kalpha)=0 are real distinct for all values of alpha then possible value of k will be a) k in (-1,0) b). k in (oo,0) c). k in (1,5) d). k in (-1,1)

Consider two function y=f(x) and y=g(x) defined as f(x)={{:(ax^(2)+b,,0lexle1),(bx+2b,,1ltxle3),((a-1)x+2c-3,,3ltxle4):} and" "g(x)={{:(cx+d,,0lexle2),(ax+3-c,,2ltxle3),(x^(2)+b+1,,3ltxle4):} underset(xrarr2)(lim)(f(x))/(|g(x)|+1) exists and f is differentiable at x = 1. The value of limit will be

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

Examine the differentiability of f(x) =2x+|x-1| at x = 1

A function f (x) is defined as follows : f(x)={{:(5+2x,"when " -(5)/(2)ltxle0),(5-2x,"when "0ltxlt(5)/(2)):} Examine the continuity and differentiability of f (x) at x= 0

The definition of the function f (x) is given below: f(x)={{:((1)/(2)-x,"when "xlt3 ),(1,"when " x=3),(x-(1)/(2),"when " xgt3):} Calculate f (3-0), f(3+0),f(3) and state whether f (x) is continuous at x =3 or not.