Which of the following statements are true if ƒ(x, y) is

Chapter , Problem 44PE

(choose chapter or problem)

Which of the following statements are true if \(f(x, y)\) is differentiable at \(\left(x_{0}, y_{0}\right)\)? Give reasons for your answers.
a. If u is a unit vector, the derivative of f at \(\left(x_{0}, y_{0}\right)\) in the direction of u is \(\left(f_{x}\left(x_{0}, y_{0}\right) i+f_{y}\left(x_{0}, y_{0}\right) j\right) \cdot u\).

b. The derivative of f at \(\left(x_{0}, y_{0}\right)\) in the direction of u is a vector.
c. The directional derivative of f at \(\left(x_{0}, y_{0}\right)\) has its greatest value in the direction of \(\nabla f\).
d. At \(\left(x_{0}, y_{0}\right)\), vector \(\nabla f\) is normal to the curve \(f(x, y)=f\left(x_{0}, y_{0}\right)\)

Equation Transcription:

∇

Text Transcription:

f(x, y)

(x_0, y_0)

(f_x (x_0 , y_0 )i + f_y (x_0, y_0 )j . u

nabla f

f(x, y)=f(x_0 , y_0 )