Point 6 of 7 — Lesson 1 – Rate of Change and Differentiation RulesQuestion bank: 43 questions (43 with pictures)
07Exam tips
Exam Secret: 'Continuity does NOT imply differentiability'. A classic example is f(x) = |x| at x = 0: it is continuous, but the left derivative is -1 while the right derivative is +1. Because left and right limits do not match, f'(0) does not exist (sharp corner).
Exam Trap: If the tangent line makes an obtuse angle with the positive x-axis, its slope m is negative (m = tan θ < 0). If θ = 90°, m is undefined (vertical tangent).
When finding the rate of change of area or volume with respect to time, always apply the Chain Rule: dA/dt = (dA/dr) · (dr/dt).
📝 Question bank for this point
43 questions linked to this point only, 43 of them with pictures.
