Practice: Tangent Planes, Gradient Vectors, Normal Lines (1)

Related Topics

Wize University Calculus 2 Textbook > Multivariable Functions

Tangent plane & Linear Approximation

4 Activities

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}T=x3e4x2+y3.

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>.<10, −4>.

Part a) The direction of the greatest decrease of temperatur

\vec u=

Part b) The rate of change of the temperatur is

I don't know

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