check monotonicity of `f(x)` at `x=0` `f(x)=x^3+2x^2+5x, xlt0; 3sinx,xgeq0`

Check monotonicity of f(x) at indicated point :(i)f(x)=x^((1)/(3)) at x=0

Which of the following function is not differentiable at x=0? f(x)=min{x ,sinx} f(x)={0,xgeq0x^2,x<0 f(x)= x^2 sgn(x)

Examine the function for continuity at x = 0 : f(x)={{:(sinx/x" when "xlt0),(x+1" when "xge0):} .

Discuss the continuity of f(x)={2x-1,\ \ \ x<0 ; {2x+1,\ \ \ xgeq0 at x=0

Which of the following function is not differentiable at x=0? f(x)={(0 ,, xgeq0),(x^2 ,, x<0):} , f(x)=x^2sgn(x)

Let f(x)=0 if xlt0,f(x)=x^(2) if xge0 , then for all x:

Prove that function f(x) = {-2x^(3)+3x^(2)-6x+5,xlt0 -x^(2)-x+1, xge0 is decreasing for all x.

Prove that function f(x) = {-2x^(3)+3x^(2)-6x+5,xlt0 -x^(2)-x+1, xge0 is decreasing for all x.

Prove that function f(x) = {-2x^(3)+3x^(2)-6x+5,xlt0 -x^(2)-x+1, xge0 is decreasing for all x.