Anyone good at math? I really need help with this Calculus problem.

[IXI Dragunz IXI]

I've been trying to figure out how to answer this question for a whole week but I can't seem to find out how to answer it:

Explain how the derivative f ' (a) can be used to estimate the value of f (x) at a point x near a.
Give an example in practical terms to illustrate your answer.

 

[RedvsBlue]

Carry the 7

 

[blumpies5]

Something to do with the slope is all I remember.....I think......maybe.......not sure. I only remember using derivatives in solving position, velocity, and acceleration problems.

 

[Trancendental]

42

 

[crunchb3rry]

Ask koalak.

 

[keithp]

The dog ate your homework?

 

[BigT]

In simplest generic terms, you could use the derivative (slope) and the original point (a, f(a)) to derive a tangent line to the curve that is defined by the function, f(x). You can use the point slope equation: y – y1 = m(x – x1) where m is the slope and the (x, y) and (x1, y1) represent the 2 different points.

Then, assuming that the next point (x) in your terminology is close to point a, we can estimate f(x) using the equation of the line derived above. Essentially, the degree to which this is accurate depends on the characteristics of the original function and depends on h being small where a + h = x.

Of course, this is a very quick and dirty technique, I am not sure if you are looking for something more complex...

A basic practical example would be estimating point acceleration from a velocity vs. time curve.