Question

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

Solution

Correct option is

The graphs of y = x and y = x3 are given in the adjoining figure.

Note that

             

Clearly f is not differentiable at x = –1, 0, 1 as there are corner points at x = –1, 0, 1.

 

SIMILAR QUESTIONS

Q1

If y2 = P(x) is a polynomial of degree 3, then    

              is equal to  

Q2

If  then the set of all points where the derivative exist is

Q3

The value of y’’ (1) if x3 – 2x2y2 + 5x + y – 5 = 0 when y(1) = 1, is equal to

Q4

If f(x, then f’(1) equals     

 

Q5

 

If f (x) = (1 + x)n, then the value of  

           

Q6

The solution set of f’(x) > g’(x) where f(x) = (1/2)52x + 1 and g(x) = 5x + 4x log 5 is  

Q7

Let f(x) = sin xg(x) = x2 and h(x) = log x.  

Q8

 up to nterms, then y’(0) is equal to

Q9

Let f and g be functions satisfying f(x) = ex g(x), f (x + y) = f (x) + f(y),g(0) = 0, g’(0) = 4 g and g’ are continuous at 0.  

Then

Q10

Which of the following functions is differentiable at x = 0?