Let `g(x)=[(3x^2-4sqrtx+1, x<1),(ax+b, x>=1))` If `g(x)` is continuous and differentiable for all numbers in its domain then (A) a=b=-4 (B) a=b=4 (C) a=4 and b =-4 (D) a=-4 and b=4

Let f:[a,b]rarr[1,infty) be a continuous function and lt g: RrarrR be defined as g(x)={(0, "if x" lt a),(int_a^x f(t)dt, "if a"lexleb),(int_a^b f(t)dt, "if x"gtb):} Then a) g(x) is continuous but not differentiable at a b) g(x) is differentiable on R c) g(x) is continuous but nut differentiable at b d) g(x) is continuous and differentiable at either a or b but not both.

Let f(x)={(-4, -4 lexlt0),(x^2-4, 0lexle4):} Discuss the continuity and differentiability of g(x)=f(|x|)+|f(x)|

If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x)=(x^(2)-x-12)(x^(2)+5x+b) , then the value of a and b , if (x+1)(x-4) is H.C.F. of f(x) and g(x) is (a) a=10 : b=6 (b) a=4 : b=12 (c) a=12 : b=4 (d) a=6 : b=10

Let f(x) = a+ b|x| + c|x|^4 where a, b and continuous are real constants . Then, f(x) is differentiable at x = 0, if

Let f(x)={x^2-4x+3, ,x<3; x-4,xgeq3 a n d g(x)={x-3,x<4; x^2+2x+2,xgeq4 Describe the function f/g and find its domain.

The number of solutions of sqrt(3x^(2)+x+5)=x-3 is (A) 0 (B) 1 (C) 2 (D) 4

Let f(x)={((x-4)/(|x-4|)+a, xlt4),(a+b, x=4),((x-4)/(|x-4|)+b,x gt 4):} Then , f (x) is continuous at x = 4, when

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

The number of points at which g(x)=1/(1+2/(f(x))) is not differentiable, where f(x)=1/(1+1/x) , is a. 1 b. 2 c. 3 d. 4

Let cos^(-1) (4x^(3) -3x) = a + b cos^(-1) x If x in [-1, -(1)/(2)) , then the value of a + b pi is