40 slides with diagrams and step-by-step worked examples. The video runs for 25 minutes 31 seconds. Pause at the practice questions before viewing the solutions.

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Slide 5: why is f′(2) = −2?

Start with f(x) = (x − 3)². Differentiate first using the chain rule:

f′(x) = 2(x − 3) × 1 = 2(x − 3).

Then substitute x = 2:

f′(2) = 2(2 − 3) = −2.

The function value is f(2) = 1, while the slope is f′(2) = −2. Increasing x slightly would decrease f, but the constraint x ≤ 2 blocks that direction at x = 2.

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