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Chapter 12: Q. 7 (page 988)

Fill in the blanks to complete each of the following theorem statements:

If f(x,y)is a function of two or three variables and Pis a point in the domain of fat which fis differentiable, then the _____ of fat Ppoints in the direction in which f_____ .

Short Answer

Expert verified

If f(x,y)is a function of two or three variables and Pis a point in the domain of fat which fis differentiable, then the gradient of fat Ppoints in the direction in which fincreases most rapidly.

Step by step solution

01

Step 1. Given information

If f(x,y)is a function of two or three variables and Pis a point in the domain of fat which fis differentiable, then the _____ of fat Ppoints in the direction in which f_____ .

02

Step 2. Filling in the blanks

If f(x,y)is a function of two or three variables and Pis a point in the domain of fat which f is differentiable, then the gradient of fat Ppoints in the direction in which f increases most rapidly.

This is because the gradient ∇fpoints in the direction in which fincreases most rapidly and the directional derivative is greatest when unit vector is parallel to the gradient.

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