Consider the function f(x,y,z) = (e^z)ln(x^2 + y^2)

a) Is there a vector r such that the directional derivative of f at (1,1,0) in the direction of r equals 1? If there is, find one such vector. If not, explain why not.

b) Is there a vector r such the directional derivative of f at (1,1,0) in the direction of r equals to -2? If there is, find one such vector. If not, explain why not.

Solution Summary

Directional derivatives are investigated. The solution is detailed and well presented.

... to t is the speed; and the second derivative of H(t ... Note: the minus sign means the direction of speed is ...Derivatives are applied to velocity and displacement. ...

... the slope of the surface at the point (3, −2,41) in the direction of the ... like to know how to find the ﬁrst-order and second-order partial derivatives of f? ...

... changes the direction from -ve to +ve direction at t = 9/2 sec --Answer. A few problems of limit are solved. Also, a few problems of first derivative which use ...

Derivative problems: Option Pricing. ... Discuss what factors would affect the price of equity and in what direction based on this option pricing view. ...

... therefore the distance in the phi-hat direction is r ... in problem 1) that the above derivatives are the ... In general, minus the derivative of the potential energy ...

... we get: (1.7) The particle start from rest, hence the initial conditions are: (1.8) The equation in the z direction is pretty simple. The derivative of with ...

... There is no force in the horizontal direction . ... Velocity is the first derivative of the position with respect to time, hence: (1.10) Thus, the initial ...

... The most common derivative products are options and ... investment vehicles and managing derivatives in ones ... three factors are "time," "direction," and "magnitude ...