Differentiability

IMPORTANT

Differentiability: Overview

This topic consists of various concepts like Differentiability of a Function,Differentiability of a Function at a Point,Concept of Tangent and its Association with Derivability, etc.

Important Questions on Differentiability

HARD
IMPORTANT

Let f(x)={sinxxx01x=0 find f''(0)(if  it  exists).

EASY
IMPORTANT

Let g(x) be a polynomial of degree one & f(x) be defined by  f x = [ g x , x 0 1 + x 2 + x 1 / x , x > 0  such that  f(x) is continuous f'1=f-1, then g(x) is

MEDIUM
IMPORTANT

Consider the function fx=x2-2x and gx=-x 
Statement-1: The composite function Fx=fgx is not derivable at x=0.
Statement-2: F'0+=2 and F'0-=-2.

HARD
IMPORTANT

Let f(x)=[n+psinx],x(0,π),nI and p is a prime number. The number of points where f( x ) is not differentiable is

( Here x represents the greatest integer less than or equal to x )

EASY
IMPORTANT

The set of all points where the function  f x = x 1 + x  is differentiable is:

HARD
IMPORTANT

For what triplets of real numbers a, b ,c with  a 0  the function fx=x,x1ax2+bx+c,otherwiseis differentiable for all x?

HARD
IMPORTANT

The number of points at which the function fx=maxa-x, a+x, b,  -<x<0<a<b can not be differentiable is

MEDIUM
IMPORTANT

If fx=sinx and gx=x3, then identify which of the following is correct for the function fgx.

EASY
IMPORTANT

If function is differentiable at x = a, find limxax2f(a)-a2f(x)x-a.

EASY
IMPORTANT

Let fx=ln x, x1

What is the derivative of fx at x=2?

EASY
IMPORTANT

Let fx=ln x, x1

What is the derivative of fx at x=0.5?

EASY
IMPORTANT

What is the derivative of cosecxo?

HARD
IMPORTANT

Let k and m be positive real numbers such that the function fx=3x2+kx+1,0<x<1mx2+k2,x1 is differentiable for all x>0. Then 8f'(8)f'18 is equal to

HARD
IMPORTANT

Let f and g be two functions defined by fx=x+1,      x<0x-1,  x0and gx=x+1,      x<01,            x0.Then gofx is

HARD
IMPORTANT

Let x denote the greatest integer function and fx=max1+x+x, 2+x, x+2x, 0x2, where f is not continuous and n be the number of points in 0, 2, where f is not differentiable. Then m+n2+2 is equal to 

MEDIUM
IMPORTANT

Let f:-2, 2 be defined by fx=xx,-2<x<0x-1x,0x<2 where x denotes the greatest integer function. If m and n respectively are the number of points in 2, 2 at which y=fx is not continuous and not differentiable, then m+n is equal to ________.  

MEDIUM
IMPORTANT

Let a and t be the greatest integer t, then the number of points, where the function fx=a+13 sinx, x0,π is not differentiable, is ____________

HARD
IMPORTANT

Consider the function fx=x2-x+x, where, ·G.I.F and · is fractional part function.

 

HARD
IMPORTANT

If fx=3x2+kx+1; 0<x<13mx2+k2;   x1 is differentiable at x=1, then 8f'8f'18 for k0 is

HARD
IMPORTANT

If fx=xsinπx;  x-1,1, then fx is (where, · is GIF)