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Grade 12 Calculus · Boss lesson · The Rule Book · about 7 minutes
Exam-hall rules, one function
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Exam-hall rules, one function

This is the boss. No calculator: the function is a bracket times a power of a bracket, (x+c)(ax+b)n(x + c)(ax + b)^n, with small whole numbers and nn equal to 2 or 3, the point is −1-1, 0, 1 or 2, and every number fits in your head. One function, one long inspection, and every answer feeds the next: read the shape and name the outer rule, name the product rule, name the chain rule for the power, find the height f(x0)f(x_0), find the slope f′(x0)f'(x_0) from the two rules you named, name the tangent line, and read off where that line crosses the yy-axis or where it sits one unit along.

Everything in the chapter rides in here: the outermost operation read before any rule runs, f′g+fg′f'g + fg' with two terms, nun−1n u^{n-1} times the inner slope with the inner slope not dropped, and the tangent line y=f(x0)+f′(x0)(x−x0)y = f(x_0) + f'(x_0)(x - x_0) from module 2 with the slope a NUMBER. Write each line down as you go; a slip in line four walks all the way to line seven. 5★ under par is the chapter crown.

no calculator in the boss room: the numbers are chosen to fit in your head