Prove that the function
If `f(x)={:{(6x-5", " x le 3),(2x^2-6x+13", " xgt3):}` is differentiable at x=3.

Discuss the continutiy of the function f(x)= {(3x+5", " x ge 2),(6x-1", " x lt 2):}

Consider the function f(x)={{:(x^(2)-5,xle3),(sqrt(x+13),xgt3):} What is the differential coefficient of f(x) at = 12 ?

Read the following information carefully and answer the question given below: Consider the function f(x)={{:(x^(2)-5,xle3),(sqrt(x+13),xgt3):} What is the differential coefficient of f(x) at x = 12?

Find the domain of the function , f(x)=(x^2 +2x +3)/(x^2 -5x +6)

f(x)={{:(3-x",","when",x le0, ),( x^(2)",", "when",xgt0):} is discontinuous at x=0

Let f(x) be a function defined as f(x)={{:(sin(x^2-3x)", "xle0),(6x+5x^2", "xgt0):} Then at x=0,f(x)

Consider the function f(x)={{:(x^(2)-5,xle3),(sqrt(x+13),xgt3):} What is lim_(xto3)f(x) equal to ?

Let f(x) be a function defined in 1lexleoo by f(x)={{:(2-x" for "1lexle2),(3x-x^(2)" for "xgt2):} What is the differentiable coefficient of f(x) at x=3 ?

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

Prove that the function f(x)=x^(3)-6x^(2)+12x-18 is increasing on R .