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Chapter 12: Q. 24 (page 953)
In Exercises , find the directional derivative of the given
function at the specified point and in the direction of the
given unit vector .
localid="1650380514741"
The directional derivative of the given
function is
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In Example 4 we found that the function has stationary points at and
(a) Use the second-derivative test to show that \(f\) has a saddle point at
(b) Use the second-derivative test to show that \(f\) has a relative minimum at
(c) Use the value of \(f(-10,0)\) to argue that \(f\) has a relative minimum at and not an absolute minimum, without using the second-derivative test.
In Exercises, by considering the function subject to the constraint you will explore a situation in which the method of Lagrange multipliers does not provide an extremum of a function.
Why does the method of Lagrange multipliers fail with this function?
Gradients: Find the gradient of the given function, and find the direction in which the function increases most rapidly at the specified point P.
Find the directional derivative of the given function at the specified point P in the direction of the given vector. Note: The given vectors may not be unit vectors.
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