Consider the real valued function of two variables with role Find . Evaluate and
ID: 2983493 • Letter: C
Question
Consider the real valued function of two variables with role
Find . Evaluate and at (1,0). Mark arrows representing the direction of these vectors at the corresponding points on a diagram of the (x,y)-plane. Calculate the directional derivative of f at the point (1,1) in the direction alpha = pi/6. What is the direction of greatest increase of f at (1,1)? Find fxx, fxy, fyy. Find the second order Taylor polynomial of f about the point (1,0). Write down the tangent plane to f at (1,0). Also find the tangent plane to f at (0,0).Explanation / Answer
let real valued function f(x,y) be x^2+y^2
df(x,y)=2x+2y
f'(1/root 2,1/2)=root 2+1
f'(1/root 2,1/2)=root 2-1
f'(1/2,0)=1
f'(1,0)=2