Exercise 1: One Step of Gradient Descent on (x-5)^2 — Possible Solution
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GIVEN
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f(x) = (x-5)^2, starting x=0, learning rate alpha=0.2

STEP 1: COMPUTE THE GRADIENT (DERIVATIVE) AT x=0
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f'(x) = 2(x-5) (power rule / chain rule, per Chapter 3)

f'(0) = 2(0-5) = 2*(-5) = -10

STEP 2: APPLY THE GRADIENT DESCENT UPDATE
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x_new = x_old - alpha * gradient
x_new = 0 - 0.2 * (-10)
x_new = 0 - (-2)
x_new = 2

RESULT
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After one step: x_new = 2

This makes sense directionally: the gradient was negative (-10),
meaning the function is DECREASING as x increases from 0 - so
gradient descent correctly moves x in the positive direction
(toward the true minimum at x=5), landing at x=2, already more
than a third of the way there in a single step.

WHY THIS WORKS AS AN ANSWER
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The gradient is computed explicitly using the derivative rule
rather than assumed, and the update formula is applied exactly as
this chapter states it, with the resulting direction of movement
checked for sensibility against the true minimum's own location.