If `f(x)={a x^2-b ,\ \ \ if\ |x|<1 1/(|x|),\ \ \ \ \ \ \ \ \ \ \ \ if\ |x|geq1` is differentiable at `x=1` , find `a ,\ bdot`

The function f(x) is defined by f(x)={x^2+a x+b\ \ \ ,\ \ \ 0lt=x 4 f is continuous them determine the value of a and b

It is given that the Rolles theorem holds for the function f(x)=x^3+b x^2+c x ,\ \ x in [1,2] at the point x=4/3 . Find the values of b and c .

If f(x)={{:(,ax^(2)-b,|x|lt 1),(,(1)/(|x|),|x| ge1):} is differentiable at x=1, then

Let A=[[3x^2], [1], [6x]],B=[a,b,c]and C=[[(x+2)^2, 5x^2, 2x],[5x^2, 2x,(x+2)^2],[ 2x,(x+2)^2, 5x^2]] be three given matrices, where a ,b ,ca n dx in Rdot Given that tr(AB)=tr(C). If f(x)=a x^2+b x+c , then the value of f(1) is ______.

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)=sin x+a^(2)x+b is an inccreasing function for all values of x, then

The graph of the polynomial f(x)=a x^2+b x+c is as shown below (Fig. 2.19). Write the signs of ' a ' and b^2-4a c . FIGURE