F(x, y) = (3 + 4xy2)i + 4x2yj, C is the arc of the hyperbola y = 1/x from (1, 1) to 2, 1 2 (a) Find a function f such that F = ∇f. f(x, y) = (b) Use part (a) to evaluate C F · dr along the given curve C.

How can the correlation in the scatter plot graph below best be described? positive correlation negative correlation both positive and negative no correlation

The figure shows the front side of a metal desk in the shape of a trapezoid. what is the area of this trapezoid? 10 ft²16 ft²32 ft²61 ft²

Find the directions in which the function increases and decreases most rapidly at upper p 0p0. then find the derivatives of the function in these directions. f(x, y)equals=x squared plus xy plus y squaredx2+xy+y2, upper p 0p0left parenthesis 1 comma negative 4 right parenthesis