Question

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

Solution

Correct option is

{–1, 0, 1}

 

f (x) = max. {xx3}. Consider the graph separately of y = x3 and y = xand find their point of intersection;     

i.e.,    x3 = x

⇒      x = 0, 1, –1 

Now, to find f (x) = max. {xx3

Neglecting the graph below the point of intersection we get the required graph of f (x) = max. {xx3}. 

Thus, from above graph, 

                      

Which shows f (x) is not differentiable at 3 points i.e., x = {–1, 0, 1}. (due to sharp edges)

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3
Q4

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

Q5

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:

Q6

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

Q7

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

Q8

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).

Q9

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

Q10

Let f (x) = Ï•(x) + ψ(x) and Ï•(a), ψ’(a) are finite and definite. Then: