# First Principles Question

• Oct 4th 2008, 12:02 PM
kamkal
First Principles Question
Hello all

I am taking an introductory calculus course at the high school level currently and had a question about first principles

basically when one finds the derivative dy/dx based on first principles, what does the answer represent??

For example, the function f(t) = -4.9t^2 + 16t + 1

when you find the derivative of this based on first principles, you get

-9.8t + 16

what can i do with the -9.8t + 16, can i use it to find instant rate of change at any value of t or no?

thanks :)
• Oct 5th 2008, 12:18 PM
Nacho
the derivative is the slop of the straight line of the curve. We suppose that in axis X is time and in axis Y is position, te slop has unit of velocity.

In your example -9.8t+16, is the slop in any instant of time, I mean, if you want find the straight line of the curve equation in t=2s, only you subtitute. Then in t=2s our original function we give a position, now you have a point and the slope, whit this you can find the straight line of the curve equation in t=2s

P.D: if you understan spanish I can explain this better
• Oct 6th 2008, 10:42 AM
kamkal
Quote:

Originally Posted by Nacho
the derivative is the slop of the straight line of the curve. We suppose that in axis X is time and in axis Y is position, te slop has unit of velocity.

In your example -9.8t+16, is the slop in any instant of time, I mean, if you want find the straight line of the curve equation in t=2s, only you subtitute. Then in t=2s our original function we give a position, now you have a point and the slope, whit this you can find the straight line of the curve equation in t=2s

P.D: if you understan spanish I can explain this better

no spanish :)

but i think i get what you are saying, this -9.8t+16 is the equation to find the slope of the tangent line which is the rate of change and in this case velocity.

thanks dude :)