Let `h(x) = min {x, x^2}`, for every real number of X. Then (A) h is continuous for all x (B) h is differentiable for all x (C) `h^'(x)` = 1, for all x > 1 (D) h is not differentiable at two values of x

Suppose that f is differentiable for all x and that f'(x) le2" for all "x," If "f(1)=2 and f(4)=8 , then f(2)has the value equal to ……….. .

Let g(x) be the inverse of an invertible function f(x), which is differentiable for all x, then g''f(x) is equal to

Let f(x) = ||x|-1|, then points where, f(x) is not differentiable is/are

Let f(x) be continuous and differentiable function for all reals and f(x + y) = f(x) - 3xy + f(y). If lim_(h to 0)(f(h))/(h) = 7 , then the value of f'(x) is

Statement I f(x) = |x| sin x is differentiable at x = 0. Statement II If g(x) is not differentiable at x = a and h(x) is differentiable at x = a, then g(x).h(x) cannot be differentiable at x = a

For every real number find all the real solutions to equation sin x + cos(a+x)+ cos (a-x)=2

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

"If "f(x)={{:(,-x-(pi)/(2),x le -(pi)/(2)),(,-cos x,-(pi)/(2) lt x le 0),(,x-1,0 lt x le 1),(,"In "x,x gt 1):} then which one of the following is not correct?(a)f(x) is continuous at x = - (pi)/(2) (b)f(x) is not differentiable at x = 0 (c)f(x) is differentiable x = 1 (d) none of them

Let f(x)={{:(,(1)/(|x|),"for "|x| gt1),(,ax^(2)+b,"for "|x| lt 1):} If f(x) is continuous and differentiable at any point, then

If f(x) = {|x|-|x-1|}^(2) , draw the graph of f(x) and discuss its continuity and differentiability of f(x)