Question

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

    easy

Solution

Correct option is

cos |x| = cos x or cos (–x). Thus is any case cos |x| = cos x for all x Ïµ R. Since h(x) = |x| is not differentiable at x = 0, so cos |x| + |x| = cos x + |x| is not differentiable at x = 0.  

           

Now f’(0–) = –2, f’(0+) = 2 so f is not differentiable at x = 0. Finally 

            

In this case g’(0+) = 0 and g’(0–) = 0.  

Thus  is differentiable at x = 0.

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

If f(x, then f’(1) equals     

 

Q4

 

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

           

Q5

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

Q6

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

Q7

 up to nterms, then y’(0) is equal to

Q8

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

Q9

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

Q10

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