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Gradient and Directional Derivative

Related Topics

Wize University Calculus 2 Textbook > Multivariable Functions

Tangent plane & Linear Approximation

4 Activities

checklist
Mark Yourself Question
  1. Grab a piece of paper and try this problem yourself.
  2. When you're done, check the "I have answered this question" box below.
  3. View the solution and report whether you got it right or wrong.
Use linear approximation to estimate the value of function f(x,y)=x2exyf(x,y)=x^2e^{xy} at point (1.01, 1.01).
More Tangent plane & Linear Approximation Questions:
Practice: Linear Approximation (1)
Find the linear approximation to z=3+x225+y249 at (1, 1)z=3+\frac{x^2}{25}+\frac{y^2}{49}~\text{at}~(1,~1).
Practice: Tangent Planes, Gradient Vectors, Normal Lines (1)
An ant is crawling along a flat concrete surface with the temperature of the surface at a point (x, y) given by T=x3e4x2+y3T=x^3e^{4x^2+y^3}.
a) At (3, -1), what is the direction of the greatest decrease of the temperature?
b) Find the rate of change of the temperature if the ant crawled from (3, -1) at speed 1 in the direction of the vector <10, −4>.<10,~-4>.