Antiderivaties

p {margin: 0; padding: 0;} No. Date Antiderivates Antiderivates with slope pields. consider y=x'+3 Y = x s or then Y'=2x Y' = 2X it doesn't matter wether the constant was 3 or -5. since when we take the drivative the constant disappears However, when we try to receise the operations: tiven y' = 2x find y=4 when x = 1 find the equation fo y Y 4 = 12 + C This is called an initial value problem 3= C We need the initial values to find the Y : X2 +3 constant Definition Slope Field A slope field or a directional field for the first order differentiable equation dy of ( (r.y) dx is a plot of short line segments with slopes f(x.y) for a lattice of points (x.y) in the plane Initial value probles and differential equations can be illustrated with a slope field