Question

Let f be a function of two variables that has continuous partial derivatives and consider the...

Let f be a function of two variables that has continuous partial derivatives and consider the points A(8, 6), B(11, 6), C(8, 10), and D(14, 14). The directional derivative of f at A in the direction of the vector AB is 9 and the directional derivative at A in the direction of AC is 8. Find the directional derivative of f at A in the direction of the vector AD. (Round your answer to two decimal places.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let f be a function of two variables that has continuous partial derivatives and consider the...
Let f be a function of two variables that has continuous partial derivatives and consider the points A(1, 1), B(7, 1), C(1, 13), D(9, 16). The directional derivative of f at A in the direction of the vector AB is 9 and the directional derivative at A in the direction of AC is 2. Find the directional derivative of f at A in the direction of the vector AD. (Round your answer to two decimal places.)
Let f(x,y) be a function of x and y. The partial derivative of f(x,y) with respect...
Let f(x,y) be a function of x and y. The partial derivative of f(x,y) with respect to y is equivalent to the directional derivative of f(x,y) in the direction of the unit vector Select one: a. 〈0,1〉 b. 〈1,0〉 c. 〈1,1,1〉 d. 〈0,5〉
​Suppose that the function f(x, y) has continuous partial derivatives fxx, fyy, and fxy at all...
​Suppose that the function f(x, y) has continuous partial derivatives fxx, fyy, and fxy at all points (x,y) near a critical points (a, b). Let D(x,y) = fxx(x, y)fyy(x,y) – (fxy(x,y))2 and suppose that D(a,b) > 0. ​(a) Show that fxx(a,b) < 0 if and only if fyy(a,b) < 0. ​(b) Show that fxx(a,b) > 0 if and only if fyy(a,b) > 0.
Suppose that  f   is a twice differentiable function and that its second partial derivatives are continuous....
Suppose that  f   is a twice differentiable function and that its second partial derivatives are continuous. Let  h(t) = f (x(t), y(t))  where  x = 2e^ t  and  y = 2t. Suppose that  fx(2, 0) = 1,  fy(2, 0) = 3,  fxx(2, 0) = 4,  fyy(2, 0) = 1,  and  fxy(2, 0) = 4. Find   d ^2h/ dt ^2  when t = 0.
Suppose that  f   is a twice differentiable function and that its second partial derivatives are continuous....
Suppose that  f   is a twice differentiable function and that its second partial derivatives are continuous. Let  h(t) = f (x(t), y(t))  where  x = 3e ^t  and  y = 2t. Suppose that  fx(3, 0) = 2,  fy(3, 0) = 1,  fxx(3, 0) = 3,  fyy(3, 0) = 2,  and  fxy(3, 0) = 1. Find   d 2h dt 2  when t = 0.
6. (5 marks) Consider the function f defined by f (x, y) = ln(x − y)....
6. Consider the function f defined by f (x, y) = ln(x − y). (a) Determine the natural domain of f. (b) Sketch the level curves of f for the values k = −2, 0, 2. (c) Find the gradient of f at the point (2,1), that is ∇f(2,1). (d) In which unit vector direction, at the point (2,1), is the directional derivative of f the smallest and what is the directional derivative in that direction?
Consider the function f(x, y) = sin(2x − 2y) (a) Solve and find the gradient of...
Consider the function f(x, y) = sin(2x − 2y) (a) Solve and find the gradient of the function. (b) Find the directional derivative of the function at the point P(π/2,π/6) in the direction of the vector v = <sqrt(3), −1>   (c) Compute the unit vector in the direction of the steepest ascent at A (π/2,π/2)
Find the directional derivative of the function f(x, y, z) = 4xy + xy3z − x...
Find the directional derivative of the function f(x, y, z) = 4xy + xy3z − x z at the point P = (2, 0, −1) in the direction of the vector v = 〈2, 9, −6〉.
] Consider the function f : R 2 → R defined by f(x, y) = x...
] Consider the function f : R 2 → R defined by f(x, y) = x ln(x + 2y). (a) Find the gradient of f(x, y) at the point P(e/3, e/3). (b) Use the gradient to find the directional derivative of f at P(e/3, e/3) in the direction of the vector ~u = h−4, 3i. (c) Find a unit vector (based at P) pointing in the direction in which f increases most rapidly at P.
s] Consider the function f : R 2 → R defined by f(x, y) = x...
s] Consider the function f : R 2 → R defined by f(x, y) = x ln(x + 2y). (a) Find the gradient of f(x, y) at the point P(e/3, e/3). (b) Use the gradient to find the directional derivative of f at P(e/3, e/3) in the direction of the vector ~u = h−4, 3i. (c) Find a unit vector (based at P) pointing in the direction in which f increases most rapidly at P.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT