If `f(x)={x ,xlt=1,x^2+b x+c ,x >1`
find b and c if function is continuous and differentiable at `x=1`

Find the cofficients a and b such that the following function f is continuous and differentiable at x=+-1: f(x)={{:((1)/(|x|)," when "|x|ge1),(ax^(2)+b," when " |x|lt1):}

Show that, the function f(x) = |x-1| is not differentiable at x = 1

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

Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be defined as g(x)={(0, "if x" lt a),(int_a^x f(t)dt, "if a"lexleb),(int_a^b f(t)dt, "if x"gtb):} Then a) g(x) is continuous but not differentiable at a b) g(x) is differentiable on R c) g(x) is continuous but nut differentiable at b d) g(x) is continuous and differentiable at either a or b but not both.

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):}

Let f(x)=(lim)_(n rarr oo)sum_(r=0)^(n-1)x/((r x+1){(r+1)x+1}) . Then (A) f(x) is continuous but not differentiable at x=0 (B) f(x) is both continuous but not differentiable at x=0 (C) f(x) is neither continuous not differentiable at x=0 (D) f(x) is a periodic function.

Which of the following is true about point of extremum x=a of function y=f(x)? (a) At x=a , function y=f(x) may be discontinuous. (b) At x=a , function y=f(x) may be continuous but non-differentiable. (c) At x=a ,function y=f(x) may have point of inflection. (d) none of these

The values of constants a and b so as to make the function f(x)={(1/|x|, |x|ge1),(ax^2+b, |x|lt1):} , continuous as well as differentiable for all x, are

Let f(x) = a+ b|x| + c|x|^4 where a, b and continuous are real constants . Then, f(x) is differentiable at x = 0, if

Let f(x)={(-,1, -2lexlt0),(x^2,-1,0lexlt2):} if g(x)=|f(x)|+f(|x|) then g(x) in (-2,2) is (A) not continuous is (B) not differential at one point (C) differential at all points (D) not differential at two points