posted by .

by determining :

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

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:


Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus - ratio test

    infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n->infinity) | [(e^n+1)/((n+1)!)] / [(e^n)/(n!)] | = lim (n->infinity) | [(e^n+1)/((n+1)!)] * [(n!)/(e^n)] | = lim (n->infinity) | ((e^n)(e^1)(n!)) …
  2. math

    bobpursley, I am confused to the equations that you have just posted. However, this is what I figured out but I'm not if it's correct. ((25+R)-B)+3N=435
  3. health

    explain from a physiological standpont how eating disorders may lead to health promblems?
  4. music

    Please can anyone help me with a musical puzzle.... I'm looking for hidden GPS coordinates within the musical notation... I know it's Figured Bass...that much I have figured out... I have read up a bit... It must start with 53... That's …
  5. Pre-Algebra

    Please let me know if I figured these out correctly. Directions: For the line with the given equation, find the slope of a parallel line and the slope of a perpendicular line. 1)y=6/5x + 144 slope of parallel: 6/5 slope of perpendicular: …
  6. statistics

    My problem is to graph a system of inequalities (which ive done) and introduce slack variables to convert the system of inequalities to a system of equations. So I am building my table and all is easy until I get to the point where …

    3. The rectangular coordinates of a point are given. Find the polar coordinates of each point. b. (0,3) I figured out a, but I canNOT figure out b. Can someone please explain?
  8. Math

    I am confused with rule of pattern 1,3,6, I figured out 10 is the next number Rule: find the difference and add 1 to the next item
  9. mathematics (urgent)

    I eventually figured out the last one, so I'll only need some help with this: The cafeteria has 144 bananas, 36 pears, and 72 apples. Each student gets the same number of pieces of fruit. What is the greatest number of students who …
  10. Math

    I have figured out x to be 2 for this system of equations but now I need help on determining the solution of the equations which are y=4x and y=2x^2. Can you please help me!

More Similar Questions