Volingatorland
I'm more of a hockey guy.
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- Jan 2, 2008
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This stems from the pick up line thread, but I wanted to attempt to explain this.
A derivative is an equation of a Function that can be used to find the slope of the tangent line of any given point on the function. A tangent line is a line of primary direction at any point on the function. the purpose of the derivative is to find the slope at a certain point, and can also be used to find velocity and acceleration. Here's a simple example.
f(x)=4x^3 + 6x
f'(x)=3x^2 +6
This means that in order to find the slope of any given point on the function f(x)=4x^3 + 6x, You simply need to plug the x value in to f'(x)
Ex:
Find the slope of the tangent line at (2, 44) [44 is the only y value when x=2, by solving the function]
Therefore:
f'(x)= 3(2)^2 + 6
= 3(4) + 6
= 12 + 6
= 18
So, the slope of the tangent line at the point (2,44) is 18, meaning the line goes up on the y-axis 18 for every 1 it moves right on the x-axis.
For those of you that are still awake, That's my best attempt to explain. I'm only in Calc I so My understanding of Derivatives are limited up to Relative Extrema at this point. Talk to me next year when I'm in Linear Algebra and I may be able to explain it better.
A derivative is an equation of a Function that can be used to find the slope of the tangent line of any given point on the function. A tangent line is a line of primary direction at any point on the function. the purpose of the derivative is to find the slope at a certain point, and can also be used to find velocity and acceleration. Here's a simple example.
f(x)=4x^3 + 6x
f'(x)=3x^2 +6
This means that in order to find the slope of any given point on the function f(x)=4x^3 + 6x, You simply need to plug the x value in to f'(x)
Ex:
Find the slope of the tangent line at (2, 44) [44 is the only y value when x=2, by solving the function]
Therefore:
f'(x)= 3(2)^2 + 6
= 3(4) + 6
= 12 + 6
= 18
So, the slope of the tangent line at the point (2,44) is 18, meaning the line goes up on the y-axis 18 for every 1 it moves right on the x-axis.
For those of you that are still awake, That's my best attempt to explain. I'm only in Calc I so My understanding of Derivatives are limited up to Relative Extrema at this point. Talk to me next year when I'm in Linear Algebra and I may be able to explain it better.
k:
