Worked solution
Find a tangent analytically and read the calculator workflow
Example 8 (Self-Reading): is the point on the curve . Find the gradient of the curve at and the equation of the tangent at this point.
CJC · Lecture · Example 8
Check the gradient analytically
Independently differentiating gives , so at the slope is 2. This verifies the printed calculator result; also satisfies the curve equation.
Read source calculator steps 1–4
Both copies print the complete workflow: press Y= and enter ; press GRAPH; press 2nd → TRACE → 6:dy/dx; enter the x-coordinate 4. The illustrated display gives dy/dx=2, X=4, Y=7. This is numerical differentiation, not a symbolic derivative or a physical calculator operation performed here.
Read source calculator steps 5–6
Press 2nd → PRGM → 5:Tangent( and enter the x-coordinate 4. The source screen draws the tangent and displays . Both Student and Teacher already include this worked result.
Write and verify the exact tangent
Using the independently checked slope 2 through , , hence . Substituting returns 7. The gradient is 2 and the tangent is .
Common mistakes
The calculator gives a numerical slope at the selected input; verify the point and line equation analytically.
Solution notes
Both source copies visually compared; source wording, displayed results and pagination retained. Independently authored analytical explanations are distinguished from printed working.