﻿ If  is differentiable at x = 0, then : Kaysons Education

# If  is Differentiable At x = 0, Then

#### Video lectures

Access over 500+ hours of video lectures 24*7, covering complete syllabus for JEE preparation.

#### Online Support

Practice over 30000+ questions starting from basic level to JEE advance level.

#### Live Doubt Clearing Session

Ask your doubts live everyday Join our live doubt clearing session conducted by our experts.

#### National Mock Tests

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

#### Organized Learning

Proper planning to complete syllabus is the key to get a decent rank in JEE.

#### Test Series/Daily assignments

Give tests to analyze your progress and evaluate where you stand in terms of your JEE preparation.

## Question

### Solution

Correct option is

p + q = 0; r is any real number

It can be seen f’(0–) = –p –q and f’(0+) = p + q. Therefore, for f to be differentiable at x = 0, we must have p + q = 0.

#### SIMILAR QUESTIONS

Q1

The set of all points where the function (x) = x |x| is differentiable is

Q2

If (2) = 4 and f’(2) = 1, then

Q3

The set of all points where the function  is differentiable is

Q4

For n Ïµ N, let  The left hand derivative of f at x = π/4 is

Q5

If f(a) = 2, f’(a) = 1, g(a) = –1 and g’(a) = 2, the value of

Q6

If f’ is differentiable function and f’’(x) is continuous at x = 0 and f’’(0) =a, the value of

Q7

Let [.] denote the greatest integer function and . Then

Q8

Let f (x + y) = (xf (y) for all x and y. If f (5) = 2 and f’(0) = 3, then f’(5) is equal to

Q9

Let f (x) = [x] and

Q10

Let

The values of the coefficient a and b for which the function is continuous and has a derivative at x0, are