Home
Class 12
MATHS
Let f(x) = {{:(int(0)^(x){5+|1-t|}dt",",...

Let `f(x) = {{:(int_(0)^(x){5+|1-t|}dt",","if",x gt 2),(5x + 1",","if",x le 2):}` Test f(x) for continuity and differentiability for all real x.

Text Solution

Verified by Experts

The correct Answer is:
x = 2
Promotional Banner

Similar Questions

Explore conceptually related problems

f(x) = {(x^(3)-3",","if" x le 2),(x^(2)+1 ",","if " x gt 2):}

f(x)= {(x^(10)-1",","if" x le 1),(x^(2)",","if" x gt 1):}

Let f(x)={{:(,(1)/(|x|),"for "|x| gt1),(,ax^(2)+b,"for "|x| lt 1):} If f(x) is continuous and differentiable at any point, then

Let f(x) = x^(4) - 8x^(3) + 22x^(2) - 24x and g(x) = {{:(min f(x)",",x le t le x + 1 -1 le x le 1),(x - 10",",x ge 1):} Discuss the continuity and differentiability of g(x) in [-1, oo)

Show that f(x) = |x-5| is continuous but not differentiable at x= 5

f(x)= {(-2",","if" x le -1),(2x",","if" -1 lt x le 1),(2",","if " x gt 1):}

f(x)= {(2x",","if" x lt 0),(0",","if" 0 le x le 1),(4x",","if" x gt 1):}

A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0):} , then f(x) is(a) continuous at x = 0 ,(b) continuous at x = 1 (c)differentiable at x = 0