Differential calculus of Functions

i got 2 Functions Y(x)=lxl^3 f(x)=x-1

1) Prove that Y can be Differentiable In point 0

2) use the information from ur Proof In 1 to Prove that the Function l(x-1)l^3
are Differentiable In point 1

thanks for helping.

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Now compute the limit from the left and the limit from the right separately. They both give 0, showing that the derivative of Y at 0 exists and is equal to 0.

For the second one use the derivative theorem about the composition of 2 functions.

If you need clarification on the right and left hand limits let me know.

but i need clarification on the right and left hand limits.

U mean from left lim -0 is still give 0
like lim 0+ is also give 0
?

thnaks

Quote:

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Originally Posted by ZOOZ

but i need clarification on the right and left hand limits. U mean from left lim -0 is still give 0
like lim 0+ is also give 0

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Yes. If h is positive, then |h| is just h. If h is negative, then |h| is -h.

So if h is positive . So the limit from the right is .

If h is negative, . So the limit from the left is .

OK thanks so much i will try alone to Solve the 2) Question.