Statement 1: `f(x)=|x-1|+|x-2|+|x-3|` has point of minima at `x=3.` Statement 2: `f(x)` is non-differentiable at `x=3.`

f(x)=|x-1|+|x-3| then f'(2) is

Let f(x)=(x^3-6x^2+12 x-8)e^xdot Statement 1: f(x) is neither maximum nor minimum at x=2. Statement 2: If a function x=2 is a point of inflection, then it is not a point of extremum.

Consider the function f(x)=|x-2|+|x-5|,c inR. Statement 1: f'(4)=0 Statement 2: f is continuous in [2,5], differentiable in

Statement 1: f(x)=(x^3)/3+(a x^2)/2 + x+5 has positive point of maxima for a<-2. Statement 2: x^2+a x+1=0 has both roots positive for a<2.

Draw the graph of f(x)=(x-1) |(x-2)(x-3)|. .

The function f(x)=x^(1/3)(x-1) has two inflection points has one point of extremum is non-differentiable has range [-3x2^(-8/3),oo)

Which of the following hold(s) good for the function f(x)=2x-3x^(2/3)? (a) f(x) has two points of extremum. (b) f(x) is convave upward AAx in Rdot (c) f(x) is non-differentiable function. (d) f(x) is continuous function.

Consider the graph of the function f(x) = x+ sqrt|x| Statement-1: The graph of y=f(x) has only one critical point Statement-2: fprime (x) vanishes only at one point

Draw the graph of the function f(x)= x- |x-x^(2)|, -1 le x le 1 and find the points of non-differentiability.

Statement 1: For f(x)=sinx ,f^(prime)(pi)=f^(prime)(3pi)dot Statement 2: For f(x)=sinx ,f(pi)=f(3pi)dot