Calculus Calculus Math Forum

September 5th, 2017, 06:32 PM   #1
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Been given this investigation and I'm wondering what the in class extensions of this may be. What are some related concepts to this? I haven't attached the last page of the investigation, which is the main part of it, but I've attached a photo of an extension I thought of, which gets the rule for a cubic function, but I want to go further and understand more. Thanks.
Attached Images image.jpg (106.2 KB, 9 views)

Last edited by skipjack; September 5th, 2017 at 10:03 PM. September 5th, 2017, 11:37 PM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,467 Thanks: 1342 I don't really know what you are asking but ... $(x+h)^n = \displaystyle \sum_{k=0}^n~\dbinom{n}{k}x^k h^{n-k}$ $(x+h)^n - x^n = \displaystyle \sum_{k=0}^{n-1}~\dbinom{n}{k}x^k h^{n-k}$ $\dfrac{(x+h)^n - x^n}{h} = \displaystyle \sum_{k=0}^{n-1}~\dbinom{n}{k}x^k h^{n-k-1}$ $\dfrac{d}{dx} x^n = \displaystyle \lim_{h\to 0} \left(\dfrac{(x+h)^n - x^n}{h}\right) = \dbinom{n}{n-1}x^{n-1} = n x^{n-1}$ Tags curve, gradient Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post oliver92 Applied Math 1 November 21st, 2015 03:43 AM DarkX132 Calculus 2 October 24th, 2014 10:24 AM mdocka1 Calculus 0 May 3rd, 2014 04:38 PM jiasyuen Calculus 3 January 9th, 2014 02:27 AM Marin Advanced Statistics 0 March 30th, 2009 01:23 PM

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