Reference no: EM131015166
Let f(x,y) = 3x2 - y + 5 (perhaps the function represents temperature distribution on the plane), and let P be the point with coordinates (1,4).
a. Sketch the level curve through P showing level value, and find a vector normal to this curve at P.
b. Find the direction (i.e. a unit vector) along which f increases most rapidly at the point P.
c. Find the rate of change of f at P along the above direction.
d. Starting from the above direction at P, if you now turn 30degrees clockwise, what will be the rate of change of f at P along this new direction?
e. Find the rate of change of f at P toward the point (2,3).
f. If y is a vector which is tangent to the level curve through P at P, what is v. Δf(1,4)? And why?
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