🎯 Limit Definition of the Derivative

Five quiz problems — polynomials, rationals, square roots, and a secant-to-tangent linear function. Each one walks the 5-step dance (Write → Expand → Subtract → Factor → Limit) so the algebra becomes muscle memory before the power rule shortcut ever enters the picture.

Problems

• Q1 · $f(x) = \dfrac{3}{x}$ — find $f'(x)$ · rational function, 4 choices
• Q2 · $f(x) = -3x + 4x^2$ — find $f'(-1)$ · polynomial, fill-in
• Q3 · $f(x) = \sqrt{x}$ — find $f'(1)$ · conjugate multiplication, rounded to nearest tenth
• Q4 · $f(x) = \dfrac{2}{x^2}$ — find $f'(2)$ · rational function, fill-in, rounded to nearest tenth
• Q5 · $f(x) = 2x + 1$ — find $f'(x)$ · linear function, 4 choices