Question

Let h(x) = min.{xx2} for every real number of x. Then:

Solution

Correct option is

h is not differentiable at two values of x

Here (x) = min {xx2} can be drown on graph in two steps. 

(a) Draw the graph of y = x and y = x2 also find their point of intersection.                                 

          i.e.x = x2 ⇒ x = 0, 1               

(b) To find h (x) = min, {xx2} neglecting the graph above the point of intersection we get, 

Thus, from the given graph,

          

Which shows h(x) is continuous for all x. But not differentiable at x = {0, 1} 

Thus, h(x) is not differentiable at two values of x.

SIMILAR QUESTIONS

Q1

, then draw the graph of f (x) in the interval [–2, 2] and discuss the continuity and differentiability in [–2, 2]

Q2

Fill in the blank, statement given below let . The set of points where f (x) is twice differentiable is ……………. .

Q3

The function f (x) = (x2 – 1) |x2 – 3x +2| + cos ( | | ) is not differentiable at

Q4
Q5

The number of points in (1, 3), where is not differentiable is:

Q6

Let f and g be differentiable function satisfying g’ (a) = 2, g (a) = b and fog = I (identity function) Then, f’(b) is equal to:

Q7

If the function , (where [.] denotes the greatest integer function) is continuous and differentiable in (4, 6), then.

Q8

Let [.] denotes the greatest integer function and f (x) = [tan2x], then:

Q9

Let f be a real function satisfying f (x + z) = f (xf (yf (zfor all real xyz . If f (2) = 4 and f’ (0) = 3. Then find f (0) and f’ (2).

Q10

Let f : R → R be a function defined by f (x) =  max. {xx3}. The set of all points where (x) is not differentiable is: