How to prove that δf(x₀,y₀,z₀) · γ'(t_0) = 0 given f(x, y,z) = x² + 4y² + 9z² and γ(t) = (x(t), y(t), z(t)) wich images is a part of the level surface x² + 4y² + 9y² = 1? (consider δf as the gradient, brain. ly does not have nabla)

Acompany manufactures large valves, packed in boxes. a shipment consists of 1500 valves packed in 75 boxes. each box has the outer dimensions 1.2 x 0.8 x 1.6 m and the inner dimensions 1.19 x 0.79 x 1.59 m. the boxes are loaded on a vehicle (truck + trailer). the available capacity in the vehicle combination is 140 m3. each valve has a volume of 0.06 m3. - calculate the load factor on the box level (%). - calculate the load factor on the vehicle level (%). - calculate the overall load factor (%).