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.

Find the directional derivative of the function at a given point P in the direction of the vector V:
f(x,y,z)= square root of xyz P(2,4,2) V=(4,2,-4)
and
f(x,y,z)= z^3 - (x^2)(y) P(1,6,2) V=(3,4,12)

Can you help with this sample question?
When computing a t-test, it is important to distinguish between directional and nondirectional hypotheses as the direction will determine the rejection regions. Describe how the rejection regions would differ according to the type of hypothesis you would use.
An insurance company ask

Let f(x,y,z)=e^(x+y+3z)
a) find the directional deriv at p(-2,2,1)in the direction of q(18,-2,4).
b) find the direction of max increase at p. what is max rate of increase?
c) find the direction of max decrease at p. what is max rate of decrease?
d) in what direction from p will f remain constant? (multiple corr

Find the directional derivative of f(x,y) = 2x^3-y^2+xy at the point (1,2) in the direction of the vector
(1,3). Be careful: That direction vector isn't a unit vector!

Consider the function :
f(x,y) = x(x-1)(x-2) + (y-1)(x-y)
[QUESTION 1]find the maximum and the minim values of the
directional derivative (df/ds)]u at ( 1 , 3/2 ) as u varies .
( (df/fs)]u : I can't write the symbol clearly but it means : the derivative of f according to s on the directi

Please help with the following abnormal psychology problem. Step by step discussions are provided.
When designing an experiment, the research hypothesis may be directional or non-directional.
1) Identify the differences between a directional and non-directional hypothesis.
2) Discuss how the directionality is relat

Thank you for the help with the last question your response helped me better understand..
Directional and nondirectional hypotheses can be easily interchanged according to the hypothesis the researcher is testing. For instance, a drug company might predict that a drug will help a subject lose weight while another drug company

Let f(x,y) = x^2 - y^3
a) Find the gradient of f(x,y) at (3,2).
b) compute the directional derivative (triangle u) f(3,2) where u is the unit vector in the direction of v = <4,3>
c) Find the maximum value of the directional derivative of f(x,y) at (3,2) and the direction in which it occurs.

(c) The diagram of FIGURE 2 shows a bi-directional opto coupler input interface circuit. When a supply voltage of 20 V is applied the LED
carries a current and 2 V is dropped across it. Calculate the value of the LED current and the value of current through the 3 k? resistance.
FIG. 2
Please refer to the attachment.