Question: (a) The function was graphed in Figure 4. Show that f x (0, 0) and f y (0, 0) both exist but f is not

(a) The function

if (x, y) + (0, 0) ху .2 f(x, y) =- + y? х if (x, y) = (0, 0)

was graphed in Figure 4. Show that fx(0, 0) and fy(0, 0) both exist but f is not differentiable at (0, 0). Use the result of Exercise 45.

(b) Explain why fx and fy are not continuous at (0, 0).

if (x, y) + (0, 0) .2 f(x, y) =- + y? if (x, y) = (0, 0)

Step by Step Solution

★★★★★

3.33 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

f0 hf00 00 h h To show that fisnt differentiable at 0 0 we need only show that f is ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

Prove that is not differentiable at (0, 0). (x, y) = (0, 0)

Q:

Prove that f(x, y) = |x, y| is not differentiable at (0, 0).

Q:

For the function f graphed in Figure 11, find the indicated limit or function value, or state that it does not exist. (a) (b) f(-3) (c) f(-1) (d) (e) f(1) (f) (g) (h) (i) Figure 11 lim f(x) limf(x)...

Q:

1. [-/3 Points] DETAILS LARCALC9 3.2.005. Find the two x-intercepts of the function f and show that f '(x) = 0 at some point between the two x-intercepts. f( x ) = x2 - 2x - 15 ( x, y ) = ( (smaller...

Q:

Find the two x-intercepts of the function f and show that f (x) = 0 at some point between the two x-intercepts. f(x) = x2 - 2x - 15 ( x, y ) = ( -3,0 ) (smaller x-value) ( x, y ) = ( 5,0 ) (larger...

Q:

Consider the graph of the function f(x) = x2 X - 56. (a) Find the equation of the secant line joining the points (-6, -14), and (B, D)' (b) Use the Mean Value Theorem to determine a point c in the...

Q:

4. [-/9 Points] DETAILS A manufacturer wants to design an open-top box having a square base and a surface area of 144 square inches. What dimensions will provide a box with maximum volume? Length of...

Q:

In Worksheet: (Topic 1. 12) ime X X -4 -3 -2 -1 0 2 3 4 8 9 f (x) 0 1 3 -5 -1 -3 5 2 -2 -6 Selected values of the continuous function f(x) are shown in the table above. Use the values in the table to...

Q:

9 10 marks Consider the graph of the function on the right a Find the domain and the range of f b List the intercepts c Find 0 and 6 d For what value of x does x 3 30 e Solve f x 0 5 a 6 3 Use your...

Q:

MCF3M - Culminating TaskDon't use parabola equations or dx/df/dp don't use any of these. Please read it carefully and answer the questions. MCF3M 1. Identify whether or not the following relation is...

Q:

Osgood Appliance Centre is advertising refrigerators for six monthly payments of $199, including a payment on the date of purchase. What cash price should Osgood accept if it would otherwise sell the...

Q:

What are the three main criteria to determine control?

Q:

Can you describe if anything is wrong with the following C + + statement? If nothing is wrong, please state so . Assume that d is an array of doubles with two rows and 1 0 columns. d [ 1 , 9 ] = 2 ....

Q:

a. The purpose or focus of the evaluation. (Incorporate a list of the questions that the evaluation sponsor wants answered or hypotheses that will be investigated.)

Q:

If a surveyor measures differences in elevation when making plans for a highway across a desert, corrections must be made for the curvature of the earth. (a) If R is the radius of the earth and L is...

Q:

In Section 4.8 we considered Newton's method for approximating a root r of the equation f(x) = 0, and from an initial approximation we obtained successive approximations x2, x3, ...., where Use...

Q:

(a) What is the difference between a sequence and a series? (b) What is a convergent series? What is a divergent series?

Q:

Suppose your company needs to raise $10 million to construct a new office building at an expanded manufacturing site. As CFO, you plan to raise the money by selling 30-year $1,000 par value bonds...

Q:

In the deal below, assume p=0.5 and a decision maker with an exponential u-curve and a risk-aversion coefficient ? = 0.001. I.e. the equation for the u-curve is ( ) , 0. x u x a be b ?? = + ? Plot...

Q:

4) A financial institution has just bought 9-month European call options on the Chinese yuan. Suppose that the spot exchange rate is 14 cents per yuan, the exercise price is 15 cents per yuan, the...