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)`

The function f(x) = x^(3) has………. .

which of the folloiwng function has point of extremum at x =0?

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

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.

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.

Consider f(x)=ax^(4)+cx^(2)+dx+e has no point o inflection Then which of the following is/are possible?

Let f: (-1,1)toR be a function defind by f(x) =max. {-absx,-sqrt(1-x^2)} . If K is the set of all points at which f is not differentiable, then K has set of all points at which f is not differentiable, then K has exactly

The diagram shows the graph of the derivative of a functin f(x) for 0 le x le 4 with f(0) = 0. Which of the following could be correct statements for y = f(x)? (a) Tangent line to y = f(x) at x = 0 makes an angle of sec^(-1) sqrt 5 with the x - axis. (b) f is increasing in (0, 3). (c) x = 1 is both an inflection point and the point of local extremum. (d) Number of critical point on y = f(x) is two.

The function f(x)=e^x+x , being differentiable and one-to-one, has a differentiable inverse f^(-1)(x)dot The value of d/(dx)(f^(-1)) at the point f(log2) is (a) 1/(1n2) (b) 1/3 (c) 1/4 (d) none of these

The critical points of the function f(x)=(x-2)^(2/3)(2x+1) are