let `f(x)=-x^3+(b^3-b^2+b-1)/(b^2+3b+2)` if `x` is `0` to `1` and `f(x)=2x-3` if `x` is `1` to `3`.All possible real values of `b` such that `f (x)` has the smallest value at `x=1` are

Let f(x)={x^3-x^2+10 x-5,xlt=1, \ -2x+(log)_2(b^2-2),x >1 Find the values of b for which f(x) has the greatest value at x=1.

If f(x) = x+ 1/x , x>0 then the greatest value of f(x) is (a) -2 (b)0 (c) 3 (d) none of these

Let f'(x)=(192x^3)/(2+sin^4pix) for all x in R with f(1/2)=0.If mleint_(1//2)^1f(x)dxleM , then the possible values of m and M are

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

Let f(x)=x+2|x+1|+2|x-1|dot If f(x)=k has exactly one real solution, then the value of k is (a) 3 (b) 0 (c) 1 (d) 2

Let f(x) = {((x^2-4)/(x+2), x lt -3), (Ina, x=-3), (a+bx, x gt -3):} . For what value of a and b is f(x) continuous on the real line?

Let f(x) = {(ax+1, x lt 1), (3, x=1), (bx^2+1, x gt 1):} . For what values of a and b is f(x) continuous at x = 1 ?

Let a and b be real numbers such the the function f(x)={(-3ax^2-2,x is differentiable for all x inR . The positive value(s) of a is (are)

Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2c x+d=0 has at least one real root lying between (0,3)dot Statement 2: If f(x) is continuous in [a,b], derivable in (a , b) such that f(a)=f(b), then there exists at least one point c in (a , b) such that f^(prime)(c)=0.

Let f(x)={(2x+a",",x ge -1),(bx^(2)+3",",x lt -1):} and g(x)={(x+4",",0 le x le 4),(-3x-2",",-2 lt x lt 0):} If a=2 and b=3, then the range of g(f(x)) is