equation of the line x = a+u₁⭑t y= b+u₂ *t Directional derivative = i + of j) • (u₁₂i + u₂j) дх ду af af D₁f= vector where vector u = (u₁,u₂ ) is a unit af i+ af ду Gradient f = dx" Example 1 f(x,y) = x²y-y² Find rate of change into direction v = <-1,3> at the point A(1,3) and find gradient of vƒ Vf(a, b) r'(1) (a, b) Level curve: f(x, y) = Zo with parameterization r(t) = (x(t), y(t)) Gradients on a Contour Map Example 2 Suppose that a bug is located on the surface described by Z = 2x²+ y² at the point P(1,1,3) and is moving into the direction a = <-2,3>. Sketch the surface and plot point P on it. Sketch direction of bug's move. a) Use directional derivative to find if the bug is ascending or descending? What is the slope of it's ascent/descent? b)What is the direction of fastest ascent? c) What is the direction of zero altitude change?