(1 point) (a) Find the point Q that is a distance 0.1 from the point P=(6,6) in the direction of v=⟨−1,1⟩. Give five decimal places in your answer. Q = ( , )

(b) Use P and Q to approximate the directional derivative of f(x, y)=√(x+3y) at P, in the direction of v.
fv ≈
(c) Give the exact value for the directional derivative you estimated in part (b).
fv =

following are the solution to the given points:

Step-by-step explanation:

In point a:

calculating unit vector:

the point Q is at a distance h from P(6,6) Here, h=0.1  

the value of Q= (5.92928 ,6.07071  )

In point b:

Calculating the directional derivative of at P in the direction of

In point C:

Computing the directional derivative using the partial derivatives of f.

the answer is 15% decrease

assuming you mean addition: addition and subtraction are reverse operations.

step-by-step explanation: