Question

Suppose that f(x) = [x], the least integer function then

Solution

Correct option is

f is continuous on [0, 1)

f is not differentiable at 1, 2, 3 (in fact not continuous) so f is not differentiable on [0, 4]. Since f does not satisfy intermediate value property so there is no differentiable function on (–∞, ∞) whose derivative is f(x). Since f is not continuous at x = 1 so f is not differentiable on [0, 1]. Also f(x) = 0 on [0, 1). Hence f is continuous on [0, 1).

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

 up to nterms, then y’(0) is equal to

Q4

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

Q5

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

Q6

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

Q7

If f is a differentiable function at a point ‘a’ and f’(a 0 then which of the following is true.

Q8

 is equal to

Q9

Which of the following could be not true if 

Q10

  is equal to