f(x)={[ax+bx^(2),;quad x<1],[4ax-2b+1;,x>=1]

If Rolle's theorem holds for the function f(x)=ax^(3)+bx^(2)+5x+1, x in [1, 2] with c=(3)/(2) , find the values of a and b.

If f(x)=ax^(2)+bx+c and f(x+1)=f(x)+x+1 , then the value of (a+b) is __

If f(x)=ax^(4)-bx^(2)+x+5 and f(-3)=2, then f(3) is

f(x)={ax^(2)+bx+c,|x|>1x+1,|x|<=1 If f(x) is continuous for all values of x, then;

If f(x)=ax^(2)+bx+c and f(x + 1) = f(x) + x + 1, then determine the values of a and b.

If the derivative of the function f(x) is every where continuous and is given by f(x)={{:(bx^(2)+ax+4,,, x ge 1), (ax^(2)+b, ,, x lt -1):}, then : a)a = 2, b = -3 b)a = 3, b = 2 c)a = -2, b = -3 d)a = -3, b= -2

If f(x)=ax^(2)+bx+c and f(x - 1) = f(x) + 2x + 1. then find the values of a and b.

If f(x) =ax^(2) +bx + c, g(x)= -ax^(2) + bx +c " where " ac ne 0 " then " f(x).g(x)=0 has