Math Is Fun Forum

kgh

Member

Registered: 2009-02-08

Posts: 11

Help with tangents

I'm trying to find the slope of the tangent when x is a. How do I simplify this?

y=2x^2+3
x=a

lim x->a  f(x) - f(a)/x-a

lim x->a  2x^2-3x-(2a^2-3a)
              ----------------------
                       x-a

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Help with tangents

You have your function as 2x^2 + 3, but are working out the slope of 2x^2 - 3x.

The methods for both are similar though, so I'll continue the second one for you, and if you wanted the other function then you should be able to find its slope yourself.

You had:

Rearrange:

Factorise:

Cancel:

As x-->a, this becomes 2(x+x) - 3, which is 4x-3.

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Why did the vector cross the road?
It wanted to be normal.

kgh

Member

Registered: 2009-02-08

Posts: 11

Re: Help with tangents

Oops that was a typo! I forgot the x in my function. Thank you very, very much!