Determine the continuity and differentiability of f(x) `f(x)=1-x` for `xlt1`; `(1-x)(2-x)` for `1leqxleq2`; `3-x` for `xgeq2`

Determine the values of x for which the following functions fails to be continuous or differentiable f(x) = {((1-x), x lt 1), ((1-x)(2-x), 1lexle2 ), ((3-x), x gt 2):}

Given f(x)={x^(2)-2x+3 for x 1 Examine the continuity and differentiability of the function f(x) at x=1

Discuss the continuity and differentiability in [ 0,2] of f(x)={|2x-3|[x], xgeq1 sin((pix)/2), x<1 to where [.] denotes the greatest integer function.

Given f(x)=cos^(-1)(sgn((2[x])/(3x-[x])) Discuss the continuity and differentiability of f (x)x=1,-1

Find the points of discontinuity, if any, of the following function: f(x)={-2 , if xlt=-1 2x , if-1

Discuss the continuity of the function f(x) given by f(x)={2-x ;\ \ \ x<2 2+x ;\ \ \ xgeq2 at x=2 .

Let f: [1,3] to R be a continuous function that is differentiable in (1,3) and f '(x) = |f(x) |^(2) + 4 for all x in (1,3). Then,

If f(x)={ax^(2)+b,x 1;b!=0, then f(x) is continuous and differentiable at x=1 if

Examine continuity at the given point of the function f defined by f(x)={(x,xlt1),(1,x=1,),(2-x,xgt1,at x =1):}