Exercise 2: The Gradient Vector and Its Magnitude — Possible Solution
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GIVEN (FROM EXERCISE 1)
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df/dx(1,2) = 12
df/dy(1,2) = -9

STEP 1: ASSEMBLE THE GRADIENT VECTOR
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Per this chapter's own definition, the gradient stacks every
partial derivative together:

grad f (1,2) = (12, -9)

STEP 2: COMPUTE ITS MAGNITUDE
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Using the standard vector magnitude formula (Linear Algebra
Fundamentals): |v| = sqrt(vx^2 + vy^2)

|grad f| = sqrt(12^2 + (-9)^2) = sqrt(144 + 81) = sqrt(225) = 15

RESULT
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Gradient vector: (12, -9)
Magnitude: 15

WHY THIS WORKS AS AN ANSWER
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The gradient is assembled directly from the two partial derivatives
computed in Exercise 1, in the exact order this chapter's own
definition specifies, and its magnitude is computed using the
standard vector-magnitude formula rather than estimated, arriving
at a clean, verifiable result.