Let `f(x) ={2x+3` for `x<=1` and `ax^2+bx` for `x>1` if `f(x)` is everywhere differentiable, prove that `f(2)=-4`.

Let f(x)=2x+3" " for xle1 =ax^(2)+bx" " for xgt1 If f(x) is everywhere differentiable, then prove that f'(2)=-4 .

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

Let f:R to R be given by f(x+y)=f(x)-f(y)+2xy+1"for all "x,y in R If f(x) is everywhere differentiable and f'(0)=1 , then f'(x)=

If f(x)={x^(2)+3x+a,quad f or x is everywhere differentiable,find the values of a and b

Let f(x)=|cos x|. Then,f(x) is everywhere differentiable (b) f(x) is everywhere continuous but not differentiable at x=n pi,n in Z(c)f(x) is everywhere continuous but not differentiable at x=(2n+1)(pi)/(2),quad n in Z(d) none of these

Let f(x)=|sinx| . Then, (a) f(x) is everywhere differentiable. (b) f(x) is everywhere continuous but not differentiable at x=n\ pi,\ n in Z (c) f(x) is everywhere continuous but not differentiable at x=(2n+1)pi/2 , n in Z . (d) none of these

Let f(x)=|cosx| (a) Then, f(x) is everywhere differentiable (b) f(x) is everywhere continuous but not differentiable at x=npi,\ \ n in Z (c) f(x) is everywhere continuous but not differentiable at x=(2n+1)\ pi/2,\ \ n in Z (d) none of these

Let f(x)=|sin x|. Then,(a) f(x) is everywhere differentiable.(b) f(x) is everywhere continuous but not differentiable at x=n pi,n in Z(c)f(x) is everywhere continuous but not differentiable at x=(2n+1)(pi)/(2),n in Z.( d) none of these

Given f'(1) = 1 and f(2x) = f(x) AA x gt 0 . If f'(x) is differentiable then prove that there exists a number c in (2, 4) such that f''(c) = - 1/8