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Title: Why are we finding slope or gradient of a point? Post by: davesf4i on Sep 20, 2012 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 Title: Why are we finding slope or gradient of a point? Post by: JulianDavis on Sep 20, 2012 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.
Title: Why are we finding slope or gradient of a point? Post by: David on Sep 20, 2012 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. Title: Why are we finding slope or gradient of a point? Post by: rkkovach on Sep 20, 2012 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. |