Define Gradient vector and directional derivative. Find the direction in which \(f(x, y) = \frac{x^2}{2} + \frac{y^2}{2}\) i. Increases and decreases…

Define Gradient vector and directional derivative.

Find the direction in which \(f(x, y) = \frac{x^2}{2} + \frac{y^2}{2}\)

i. Increases and decreases most rapidly at the point (1,1)

ii. What is the direction of zero change in \(f\) at (1,1)?

iii. Derivative of \(f(x, y)\) at the point (1,1) in the direction \(v = 3i - 4j\).