Answer:
The directional derivative of f is 4√3 - 9/2
Step-by-step explanation:
∵ Du f(x,y) = fx(x,y) · a + fy(x,y) · b
∵ The unit vector in the direction of Ф is <a , b>
∵ f(x , y) = 8x + 9y at the point (9 , 1) in the direction Ф = -π/6
∵ df/dx = 8 , df/dy = 9
∴ Du f(x,y) = 8 · a + 9 · b
∵ The unit vector U = <cos(-π/6) , sin(-π/6)> = <√3/2 , -1/2>
∴ Du f(9,1) = 8(√3/2) + 9(-1/2) = 4√3 - 9/2
