Home
Class 12
MATHS
Show that the function f(x) = {{:(-x^2, ...

Show that the function `f(x) = {{:(-x^2, x le 0),(x^2 ,x gt 0):}` is continuous at `x = 0`. Also show that f is differentiable at `x = 0`.

Text Solution

Verified by Experts

The correct Answer is:
f is also differentiable at `x = 0`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Short Answer Type Questions)(Section IV)|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Short Answer Type Questions)(Section V)|23 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Short Answer Type Questions)(Section II)|16 Videos

  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE |73 Videos

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )|45 Videos

Similar Questions

Explore conceptually related problems

Show that the function f(x) = {:{(|x|, x le2),([x],x>2):} is continouous on [0,2]

Prove that the function f(x) = {:{((sinx)/x , x < 0),(x^2 +1, x ge0):} is continuous.

Show that the function f(x) = {{:(x^2 + 3 , "if" x != 0),(1,"if" x = 0):} is not continous at x = 0 .

Show that the function f(x) = {{:(2 + x"," , "if " x ge 0),(1",", "if " x lt 0):} is not continuous at x = 0

Show that the function: f(x) = {:{(2+x,ifxge0),(2-x,ifx<0):} is continuous but not derivable at x=0

Show that the function f(x) = {:{(x^n sin(1/x), x ne 0),(0, x = 0):} is continuous but not differentiable at x= 0.

Discuss the continuity of the function f(x) = {:{(x^2, x le 0),(1-x,x>0):} at x = 0

Show that the function f given by: f(x)={(x^3,+,3,,if x ne 0),(1,,,,if x=0 is not continuous at x=0

Show that the function 'f' given by: f(x) = |x| + |x-1|, x in R is continuous both at x = 0 and x=1