Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Roots of a Function

Hi guys,

There's something I'm wondering how to prove algebraically. If we have a function with two equal roots, then we know that at the root, the gradient must be zero, so the derivative of that function, at the root, must surely be zero as well. My question is, how do I prove this algebraically, rather than just with common sense?

Thanks

Last edited by Au101 (2011-08-01 10:05:25)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,649

Re: Roots of a Function

hi Au101

Here's an example that'll show why it happens:

The product rule causes (x-2) to be a factor of the differentiated function.

It seems to me that'll always happen, so change the 2s and 4 into letters and you've got your proof.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Roots of a Function

That sounds great to me, thanks.