Question

Let $f(x,y) = \ln(y - x^2)$ and let P be the point with coordinates $(2,5)$. (a) Find the directional derivative of f at P in the direction of $\vec{a} = 4\hat{i} - 3\hat{j}$. (b) Find a unit vector in the direction in which f increases most rapidly at P, and find the rate of change of f in that direction.

          Let $f(x,y) = \ln(y - x^2)$ and let P be the point with coordinates $(2,5)$. 
(a) Find the directional derivative of f at P in the direction of $\vec{a} = 4\hat{i} - 3\hat{j}$.
(b) Find a unit vector in the direction in which f increases most rapidly at P, and find the rate of change of f in that direction.

Let f(x,y) = ln(y - x^2) and let P be the point with coordinates (2,5).
(a) Find the directional derivative of f at P in the direction of a⃗ = 4î - 3ĵ.
(b) Find a unit vector in the direction in which f increases most rapidly at P, and find the rate of change of f in that direction.

Added by Timothy F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

03/24/2022

Step 1

The gradient of f is given by the vector (∂f/∂x, ∂f/∂y). Show more…

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PLEASE HELP!!! WILL UPVOTE Let fx,y=lny-x and let P be the point with coordinates 2,5 Find the directional derivative of f at P in the direction of a=4i-3j bFind a unit vector in the direction in which f increases most rapidly at P,and find the rate of change off in that direction.