Question

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.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
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.
​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.
Find all second partial derivatives of f : ?(?, ?, ?) = ?^??^??^? fx= fy= fz=...
Find all second partial derivatives of f : ?(?, ?, ?) = ?^??^??^? fx= fy= fz= fxx= fyy= fzz= fxy= fxz= fyz=
(1 point) Find all the first and second order partial derivatives of f(x,y)=7sin(2x+y)−2cos(x−y) A. ∂f∂x=fx=∂f∂x=fx= B....
(1 point) Find all the first and second order partial derivatives of f(x,y)=7sin(2x+y)−2cos(x−y) A. ∂f∂x=fx=∂f∂x=fx= B. ∂f∂y=fy=∂f∂y=fy= C. ∂2f∂x2=fxx=∂2f∂x2=fxx= D. ∂2f∂y2=fyy=∂2f∂y2=fyy= E. ∂2f∂x∂y=fyx=∂2f∂x∂y=fyx= F. ∂2f∂y∂x=fxy=∂2f∂y∂x=fxy=
part 1) Find the partial derivatives of the function f(x,y)=xsin(7x^6y): fx(x,y)= fy(x,y)= part 2) Find the...
part 1) Find the partial derivatives of the function f(x,y)=xsin(7x^6y): fx(x,y)= fy(x,y)= part 2) Find the partial derivatives of the function f(x,y)=x^6y^6/x^2+y^2 fx(x,y)= fy(x,y)= part 3) Find all first- and second-order partial derivatives of the function f(x,y)=2x^2y^2−2x^2+5y fx(x,y)= fy(x,y)= fxx(x,y)= fxy(x,y)= fyy(x,y)= part 4) Find all first- and second-order partial derivatives of the function f(x,y)=9ye^(3x) fx(x,y)= fy(x,y)= fxx(x,y)= fxy(x,y)= fyy(x,y)= part 5) For the function given below, find the numbers (x,y) such that fx(x,y)=0 and fy(x,y)=0 f(x,y)=6x^2+23y^2+23xy+4x−2 Answer: x= and...
Please find ALL second partial derivatives of f: fx, fy, fz, fxx, fyy, fzz, fxy, fxz,...
Please find ALL second partial derivatives of f: fx, fy, fz, fxx, fyy, fzz, fxy, fxz, and fyz For ?(?, ?, ?) = (?^?)(?^?)(?^?) THANK YOU
Let f(x, y) = 2x^3y^2 + 3xy^3 4x^3 y. Find (a) fx (c) fxx (b) fy...
Let f(x, y) = 2x^3y^2 + 3xy^3 4x^3 y. Find (a) fx (c) fxx (b) fy (d) fyy (e) fxy (f) fyx
Given w=f(x,y,z) List all of the second and third derivatives. How many unique second derivatives? How...
Given w=f(x,y,z) List all of the second and third derivatives. How many unique second derivatives? How many unique third derivatives? Example: If z=f(x,y) , then z has 3 unique derivatives. fxx, fxy. fyy
Let f(x,y,z)=exy4z5+xy2+y3z Calculate. fx fy fz fxx fxy fyy fxz fyz fzz fzyy fxxy fxxyz 1
Let f(x,y,z)=exy4z5+xy2+y3z Calculate. fx fy fz fxx fxy fyy fxz fyz fzz fzyy fxxy fxxyz 1
Consider the function f(x,y) = xe^((x^2)-(y^2)) (a) Find f(1,−1), fx(1,−1), fy(1,−1). Use these values to find...
Consider the function f(x,y) = xe^((x^2)-(y^2)) (a) Find f(1,−1), fx(1,−1), fy(1,−1). Use these values to find a linear approximation for f (1.1, −0.9). (b) Find fxx(1, −1), fxy(1, −1), fyy(1, −1). Use these values to find a quadratic approximation for f(1.1,−0.9).