Week Five Multivariable Calculus 1

Question 1

What are contours

Answer 1

Contours are curves in the (x,y) plane on which the function has a given constant value.
F(x,y) = C

Question 2

How do you find the gradient or grad f

Answer 2

You take the partial derivative of x and y and then you put it into a column matrix.

Question 3

What does the grad f

Answer 3

A vector which points in the direction of the greatest increase in the plane.
And
It’s magnitude also equals the max rate of change.

Question 4

What is the formula for the tangent plane.

Answer 4

Tangent plane z = F(x0 ,y0) + ( x - x0) *gradF|x=x0