Let f be a function of two variables that has continuous partial derivatives and consider the points A(8, 9),

B(10, 9),

C(8, 10),

and

D(11, 13).

The directional derivative of f at A in the direction of the vector AB is 9 and the directional derivative at A in the direction of

AC is 2. Find the directional derivative of f at A in the direction of the vector AD.

(Round your answer to two decimal places.)

The directional derivative of f at A in the direction of AD is 7.

Step-by-step explanation:

Step 1:

Directional of a function f in direction of the unit vector is denoted by ,

.

Now the given points are

,

Step 2:

The vectors are given as

AB = (10-8, 9-9),the direction is

AC=(8-8,10-9), the direction is

AC=(11-8,13-9), the direction is

Step 3:

The given directional derivative of f at A is 9,

The given directional derivative of f at A is 2,

The given directional derivative of f at A is

The directional derivative of f at A in the direction of   is  7.

b) 36

step-by-step explanation:

18 times 2 is 36

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