Set y equal to zero and look at how the derivative behaves along the x-axis. Do the same for the y-axis by setting x equal to 0 Consider the curve in the plane defined by setting y = 0 -- this should correspond to the points in the picture where the slope is zero. Setting y equal to a constant other than zero gives the curve of points where the slope is that constant. These are called isoclines, and an be used to construct the direction field picture by hand. (2x + y) (2y) 2. y = 2y + x²e2x 1. y' = 3. y = e-*+ 2y 4. y = 2 sin(x) +1+y

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: