SOLUTION: Verify that the obtained function is smooth at all points in your domain: f(x)={ 2 , if 0≤x≤2.72 -----{ln(x^2),if 2.72< x

SOLUTION: Verify that the obtained function is smooth at all points in your domain: f(x)={ 2 , if 0≤x≤2.72 -----{ln(x^2),if 2.72< x < 20

Question 1184358: Verify that the obtained function is smooth at all points in your domain:
f(x)={ 2 , if 0≤x≤2.72
-----{ln(x^2),if 2.72< x < 20
-------{ x-14 , if 20≤x≤25
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!

No, your function is not smooth in the domain [0, 25]. In fact, it's not even continuous.
What makes it continuous is the following definition:

.
But even with the correct definition it still is not smooth, as the function is not differentiable at and
At , the left-hand derivative is , while the right-hand derivative is , so the derivative at does not exist.

At , the left-hand derivative is , while the right-hand derivative is , so the derivative at does not exist.

RELATED QUESTIONS
Create a function piecewise and verify that the function is uniform throughout the domain (answered by robertb)

Find the domain of the rational function f(x)=2x^2-4/3x^2+6x-72 (answered by solver91311)

Please help. Find all real numbers that are not in the domain of the following function. (answered by Theo)

find all zeros of the function.... (answered by ewatrrr)

x^2-x=72 (answered by jim_thompson5910)

find the domain of the function. f(x)= ln(x^2-9 /... (answered by ikleyn)

Solve by factoring: x+x(raised to the 1/2 power)-72=0 {{{x+x^(1/2)-72=0}}} PLEASE show... (answered by richwmiller)

x^2+6x-72=0 (answered by Alan3354,london maths tutor)

12^(x+2)=72 (answered by Alan3354,ankor@dixie-net.com,MathLover1,MathTherapy)