Which of the following statements are true if (x, y) is differentiable at (x 0 , y

Which of the following statements are true if ƒ(x, y) is differentiable at (x₀, y₀)? Give reasons for your answers.

a. If u is a unit vector, the derivative of ƒ at (x₀ , y₀) in the direction of u is (ƒ_x(x₀, y₀)i + ƒ_y(x₀, y₀)j) · u.

b. The derivative of ƒ at (x₀, y₀) in the direction of u is a vector.

c. The directional derivative of ƒ at (x₀, y₀) has its greatest value in the direction of ∇ƒ.

d. At (x₀, y₀), vector ∇ƒ is normal to the curve ƒ(x, y) = ƒ(x₀, y₀).