Let `f(x)={ax(x-1)+b ; x<1 and `x + 2` ; 1<=x<=3 , px^2 +qx+2 ; x> 3` is contnuous `AA x in R` except `x-1 and |f(x)|` is differentiable every where and `f'(x)` is continuous at `x=3`.

"Let "f(x)=phi(x)+Psi(x) where, phi'(x) and Psi'(x) are finite and definite. Then, a. f(x) is continuous at x = a b. f(x) is differentiable at x = a c. f'(x) is continuous at x = a d. f'(x) is differentiable at x = a

Let f : R to R be defined by f (x + y) = f (x) - f (y) + 2xy + 1 AA x, y in R . If f (x) is differentiable every where and f '(0) =1, find f '(x).

If f(x) be such that f(x) = max (|3 - x|, 3 - x^(3)) , then (a) f(x) is continuous AA x in R (b) f(x) is differentiable AA x in R (c) f(x) is non-differentiable at three points only (d) f(x) is non-differentiable at four points only

If f(x) = 3(2x + 3)^(2//3) + 2x + 3 , then: (a) f(x) is continuous but not differentiable at x = - (3)/(2) (b) f(x) is differentiable at x = 0 (c) f(x) is continuous at x = 0 (d) f(x) is differentiable but not continuous at x = - (3)/(2)

Let f(x) = {{:(min{x, x^(2)}, x >= 0),(max{2x, x^(2)-1}, x (A) f(x) is continuous at x=0 (B) f(x) is differentiable at x=1 (C) f(x) is not differentiable at exactly three point (D) f(x) is every where continuous

let f:R rarr R be a continuous function AA x in R and f(x)=5,AA x in irrational. Then the value of f(3) is

Let f(x)={1, x =1 . Then, f is (a) continuous at x=-1 (b) differentiable at x=-1 (c) everywhere continuous (d) everywhere differentiable

Let f(x+y)=f(x)+f(y)AA x, y in R If f(x) is continous at x = 0, then f(x) is continuous at

Let f(x)=ax+1,x For what values of a and b is f(x) continuous at x=1