- #1

Chenkel

- 482

- 108

Hello everyone, I've been brushing up on some calculus and had some new questions come to mind.

I notice that most proofs of the fundamental theorem of calculus (the one stating the derivative of the accumulation function of f is equal to f itself) only use a limit where the derivative is approached from the right for calculating the derivative of the accumulation function.

Generally speaking I've been mostly satisfied with the proofs but I'm wondering about a derivation of this derivative when approaching x from the left. The derivative of the accumulation function regardless of if the derivative is approached from the left or from the right should be equal, right?

When can we trust a derivative approached from the right is the same as the derivative when the derivative is approached from the left?

If anyone can elucidate me on this matter I will appreciate it.

Thank you and let me know what you think!

I notice that most proofs of the fundamental theorem of calculus (the one stating the derivative of the accumulation function of f is equal to f itself) only use a limit where the derivative is approached from the right for calculating the derivative of the accumulation function.

Generally speaking I've been mostly satisfied with the proofs but I'm wondering about a derivation of this derivative when approaching x from the left. The derivative of the accumulation function regardless of if the derivative is approached from the left or from the right should be equal, right?

When can we trust a derivative approached from the right is the same as the derivative when the derivative is approached from the left?

If anyone can elucidate me on this matter I will appreciate it.

Thank you and let me know what you think!

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