[" (d) none of these "],[" If "f(x)=a|sin x|+be^(|x|)+c|x|^(3)" and if "f(x)" is differentiable at "x=0" ,then "]

If f(x)=a|sinx|+be^|x|+c|x|^3 and if f(x) is differentiable at x=0 then

Show that f(x) = |x| sin x is differentiable at x=0.

The function f(x)=a sin |x| +be^|x| is differentiable at x=0 when

Show that the functions f (x) = x ^(3) sin ((1)/(x)) for x ne 0, f (0) =0 is differentiable at x =0.

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

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

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)=a+b|x|+c|x|^(4), where a,b and c are real constants.Then,f(x) is differentiable at x=0, if a=0 (b) b=0( c) c=0(d) none of these