Question

Let h(x) – min (xx2) for every real number of x. then which one is true,

Solution

Correct option is

h is not differentiable at two value of x.

Here h (x) = min {xx2} can be drawn 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

The number of real solutions of the equation ex + x = 0 is:

Q2

The number of real solutions of the equation

                  

Q3

The number of solution of the equation 

Q4

How many roots does the following equation possess 

Q5

The number of real solution of the equation

            

Q6

Number of solution of  is equal to:

Q7

Number of roots of 

Q8
Q9

The number of solution of the equation

               

where [.] denotes the greatest integer function is: