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Home Q & A Board Science-Related Homework Help Mathematics
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davesf4i davesf4i
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11 years ago
What is the actual meaning of slope
Please don't say as rise/run or y2-y1/x2-x1

What is its actual meaning and what is its scope

And what is the meaning of successive differentiation
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#1
11 years ago
Slope is rate of change. It's important because there are numerous relationships in nature that involve rates of change. For example, velocity is the derivative of position and acceleration is the derivative of velocity. Those are just some simple examples. We can describe wave motion, the dispersion of heat, and many other things in nature using the rates of change.
 
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#2
11 years ago
It is a measure of how steep the line rises and is actually the tangent of the angle the line makes with the x- axis.

ie gradient = 1 is a line at 45 degrees ro direction x

If you differentiate the equation of the line y=mx +c

dy/dx = m    ie the gradient.

If you differntiate this again yo get zero because the gradient does not chane.

If you differentiate the equation for a parabola  y  =  ax^2, you get 2ax so the gradient is different for different values of x.
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#3
11 years ago
Slope is the measure of change. The steepness of the slope tells you
whether the change is gradual or fast.
The first derivative tells you how fast at any point on the curve. It is
called velocity.
The second derivative tells you how fast it is speeding up or slowing down.
It is a measure of the rate of change of change, or velocity. It is called
acceleration, or deceleration.
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