Watch the slope readout while the tangent slides. Let them predict first.
Answer: the flat points are x = -1 and x = 1, where f'(x) = 0.
Tie the sign of the slope's change to the shape: cap or cup.
One observation x = 3. Let them predict first.
Answer: at the same beta, 1.5. A log does not move the location of the peak.
Go line by line. Write the intermediate step; that is where the 2022 slip happened.
Watch the slope readout while the tangent slides along the log-likelihood. Let them predict first.
Answer: the score is zero at beta-hat = x/2 = 1.5, where the tangent is flat.
Three observations x = 3, 1, 2. Let them predict first.
Answer: log of the product is the sum of the logs; the peak is at xbar/2 = 1.
Five boxes. The example row uses x = 3 from the earlier slides.
Repeat the five take-aways, then send them to the drills.