[" If "f(x)={[ax^(2)-b," when "0<=x<1],[2," when "x=1],[x+1," when "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)=ax^(2)+bx+c , show that , underset(hrarr0)"lim"(f(x+h)-f(x))/(h)=2ax+b

Let f(x)=ax^(2)-b|x| , where a and b are constant . Then at x=0 , f(x) has

Let f(x) =ax^(2) -b|x| , where a and b are constants. Then at x = 0, f (x) is

which of the following graph represents the expression f(x)=ax^(2)+bx+c(a!=0) when a>0,b<0$c<0?

A continuous function f(x) is defined as follows : f(x)={{:(x,"when "xlt1),(ax+bx^(2),"when "1lexle2),(2x^(2),"when "xgt2):} Find the values of a and b.

The function f(x) Is defined as follows : f(x)={{:(x^(2)+ax+b" , "0lexlt2),(3x+2" , "2lexle4),(2ax+5b" , "4ltxle8):} . If f(x) is continuous on [0,8], find the values of 'a' and 'b'.

If (x-2)and(x-3) are two factors of f(x)=x^(3)+ax+b , then find the remainder when f(x) is divided by x-5 .