The paragraph says, " Even if the function f is an everywhere differentiable function, it is still possible for f ' to be discountinuous. However, the graph of f ' can never exhibit a discountinuity of ...." picture is in paint document...(adsbygoogle = window.adsbygoogle || []).push({});

What type of discountinuity is that? a hole discountinuity?

second Question: Is my understanding correct? This is my explanation why f is not differentiable at some x value.

Given

f ' (x) =

x , x>0

x^2 x<0

7 , x = 0.

Therefore, the graph of the differnetiable function should have a similar discontinuity as the one shown in the paint document. (Determining the limit)

lim f ' (x) as x → 0- = lim f ' (x) as x → 0+ = 0 however because lim Δx → 0 [ f(0 + Δx) - f(0) ]/Δx is equal to f ' (0) = 7 ≠ 0, therefore the function f non differentiable at x = 0 because inorder for f to be diff at 0, f'(0) must equal 0

Is my understanding why f is not differentiable at x = 0 correct?

Next, If I wanted to make f differentiable at x could I do this by defining one of two functions....

f ' (x) =

x , x>0

x^2 x<0

0 , x = 0.

OR

f ' (x) =

x , x>0

x^2 x<0

Would this work to make f diff at x = 0?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Limit Questioin

**Physics Forums | Science Articles, Homework Help, Discussion**