Monday
March 30, 2015

Homework Help: differentiation

Posted by Emma on Friday, May 25, 2007 at 7:25am.

by determining :

lim f(x+h)-f(x)
h->0 ---------------
h

show that if f(x)=2x^2+2 then dy/dx=4x.

i figured out that f'(x) is 4x...but i am confused about what to do next...someone help?

"i figured out that f'(x) is 4x..."

That's the answer! dy/dx is just a notation for the derivative. If the function f(x) is dentoted by y, then

f(x+h)-f(x) can be called Delta y (i.e. a change in y) and h is, of course, a change in x, which we can denote as Delta x. So, the ratio

[f(x+h)-f(x)]/h can also be written as:

Delta y/Delta x

The derivative is obtained by taking the limit Delta x--->0. The notation for this limiting case is dy/dx

This notation dates back from the time before limits were invented. dy and dx were taken to be infinitesimal quantities, i.e. smaller than any positive number, yet larger than zero. When mathematics was further developed in the 19-th century it was found that infinitesimal numbers were an ill defined concept and limits were invented to do calculus.

The notation dy/dx for the derivative was kept but you could no longer interpret it as a ratio of two well defined quantities dy and dx.

However, in the 1960s Abraham Robinson showed how one can rigorously define infinitesimal numbers, see here:

http://en.wikipedia.org/wiki/Hyperreal_number

Answer this Question

First Name:
School Subject:
Answer:

Related Questions

Math - I am confused with rule of pattern 1,3,6, I figured out 10 is the next ...
calculus - ratio test - infinity of the summation n=1: (e^n)/(n!) [using the ...
TRIGONOMETRY - 3. The rectangular coordinates of a point are given. Find the ...
mathematics (urgent) - I eventually figured out the last one, so I'll only need ...
Math - I have figured out x to be 2 for this system of equations but now I need ...
Pre-Algebra - Please let me know if I figured these out correctly. Directions: ...
math - bobpursley, I am confused to the equations that you have just posted. ...
music - Please can anyone help me with a musical puzzle.... I'm looking for ...
statistics - My problem is to graph a system of inequalities (which ive done) ...
health - explain from a physiological standpont how eating disorders may lead to...

Members