Interphase Calc - Week 2

Gradient Vector

vector created when combining all partial derivatives of f(x)… nabla

-thegradient has the interpretation that it provides the direction of max increase of the function f. What this means is that if we are currently standing at the point (1, 2) in the example just conducted, then we should head in the direction (4, 1) to increase our altitude as fast as possible

-the gradient of a function f is perpendicular to the level curves of the function itself.

L(x, y) = f(4, 3) + fx(4, 3)(x − 4) + fy(4, 3)(y − 3).

Linear approximation

… f is differential at x₀ if f(x₀+h) ≅ f(x₀) + (x - x₀) ⋅ ∇f(x₀)

Tangent plane

Multivariate Chain Rule

dz/dt = (∂z/∂x) * (dx/dt) + (∂z/∂y) * (dy/dt)