Q. 61. - Calculus

Question

Ian is travelling along a glacier. The elevation of the glacier

in his area is described by the function

$f (x, y) = 1.2 - 0.2x^2- 0.3y^2 + 0.1xy - 0.25x$,

where $x,y$ and f are given in miles.

(a) What is the direction that Ian would need to go

to descend most steeply if he is at the point

$\left(0.5,-0.5\right)$?

(b) In what direction would Ian have to turn in order to

contour (i.e., , neither ascend nor descend) across the

glacier?

Step-by-Step Solution

Answer

ab cd

step 1

step 2

Step 2: Identify geometric figures and given information

Identify shapes, angles, lengths, and relationships.

Step 3: Apply geometric formulas and theorems

Use appropriate formulas and theorems to set up equations.

Step 4: Solve and compute

Solve equations and compute required quantities.

Step 5: State the final answer

Express the answer with correct units.