1. At the point (-1,2), the function $f(x, y)$ increases most rapidly in the direction of
(-3,4) at the rate of change equals to 10. Find the directional derivative of $f$ at
(-1,2) in the direction of (4, -3).
2. Let $f(x, y) = \sin(x) - y$. Sketch the level curves $f(x, y) = c$ for $c = -1, 0, 1$. Draw the
gradient vectors $\nabla f$ at some typical points on the level curve $f(x,y) = 0$. Write an
equation for the tangent line of the level curve $f(x, y) = 1$ at the point $(\frac{\pi}{6}, -\frac{1}{2})$.