Questions
BN5206 Week 5 online quiz
Single choice
Given the following function f(x,y)=3x2+y2+1 The gradient of f at (x,y) = (1,1) is
Options
A.[4
1]
B.[7
2]
C.[6
2]
D.[5
1]
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Step-by-Step Analysis
To determine the gradient, I first identify the given function: f(x, y) = 3x^2 + y^2 + 1. The gradient ∇f is the vector of its partial derivatives: (∂f/∂x, ∂f/∂y).
∂f/∂x = 6x because the derivative of 3x^2 with respect to x is 6x, and the rest does not depend on x.
∂f/∂y =......Login to view full explanationLog in for full answers
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Similar Questions
Please select all the correct statements about the gradient.
Given the following function The gradient of f at (x,y) = (1,1) is
Tasks: Let's continue taking partial derivatives. Go to Example 11.3 and work through yourself how the three derivatives (with respect to 𝑥 , 𝑦 , and 𝑧 ) were computed. At the end of Example 11.3 we are also introduced to the definition of the gradient of a function. If 𝑓 is a function of 𝑛 variables and all the partial derivatives exist, then the gradient of 𝑓 is defined to be ∇ 𝑓 ( 𝑥 ) = ( ∂ 𝑓 ∂ 𝑥 1 ( 𝑥 ) , ∂ 𝑓 ∂ 𝑥 2 ( 𝑥 ) , … , ∂ 𝑓 ∂ 𝑥 𝑛 ( 𝑥 ) ) . This video goes over the definition and some facts on notation: Question: Which of the following functions have gradient ∇ 𝑓 = ( 𝑦 𝑒 𝑥 𝑦 + 𝑦 , 𝑥 𝑒 𝑥 𝑦 + 𝑥 ) ?
Given the following function f(x,y)=3x2+y2+1 The gradient of f at (x,y) = (1,1) is
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