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`

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

If f(x)={x ,\ xlt=1x^2+b x+c ,\ x >1 , then find the values of b\ a n d\ c if f(x) differentiability at x=1.

If f(x)={(x","xle1,),(x^2+bx+c",",xgt1):} then find the values of b and c if f(x) is diferentiable at x=1.

Let f(x)={1, xlt=-1|x|, -1

Let f(x)={(1/(|x|), for |x| ge 1),(ax^2+b,for |x| < 1)) . If f(x) is continuous and differentiable at any point, then (A) a=1/2, b=-3/2 (B) a=-1/2, b=3/2 (C) a=1,b=-1 (D) none of these

The function f(x)={{-x^(2)+6, if 0<=x<2 },{ x-1, if 2<=x<=4 }, then find if f(x) is continuous, differentiable or both.

Let f(x)=sin^(-1)((2x)/(1+x^(2)))AA x in R. The function f(x) is continuous everywhere but not differentiable at x is/ are

The function f : R rarr R given by f(x) = - |x-1| is (a) continuous as well as differentiable at x = 1 (b) not continuous but differentiable at x = 1 (c) continous but not differentiable at x = 1 (d) neither continous nor differentiable at x = 1