Find the Direction in Which the Maximum Rate of Change $f ( x , y ) = 2 \sin ( x y ) , ( 1,0 )$

question 27

Multiple Choice

Find the direction in which the maximum rate of change of f at the given point occurs. $f ( x , y ) = 2 \sin ( x y ) , ( 1,0 )$

• A) \(\langle2,0 \rangle\)
• B) \(\langle1 , - \sqrt { 2 } \rangle\)
• C) \(\langle \sqrt { 2 } , 0 \rangle\)
• D) \(\langle0,2 \rangle\)
• E) \(\left\langle\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right\rangle\)

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Definitions:

Perfect Cube

A number that can be expressed as the cube of an integer.

Neither

Indicates a situation or condition where none of the specified alternatives or options apply.

Cube Roots

The number that when multiplied by itself twice gives the original number. Symbolically, the cube root of \(x\) is \(x^{1/3}\).

Perfect Cube

A value that represents the result of cubing an integer.