Lesson 1 Questions: Rate of Change and Differentiation Rules — Lesson quiz

The slope of the tangent to y = x² − 6x + 5 at the point (4, −3) is:

If y = (2x + 1)(3x − 4), then dy/dx at x = 1 equals:

Using the quotient rule, the derivative of (x + 3)/(x − 2) for x ≠ 2 is:

If y = (3x² − 5)⁴, then dy/dx is:

The derivative of sin(3x) with respect to x is:

For s(t) = t³ − 6t² + 9t metres, the particle is momentarily at rest at:

The tangent to y = x³ at the point (1, 1) is:

The second derivative of y = x⁴ − 2x³ + 5 is:

For f(x) = |x − 3|, the derivative f′(3) is:

For f(x) = 2x³ − 9x² + 12x + 1, the local maximum occurs at x =

The inflection point of f(x) = 2x³ − 9x² + 12x + 1 is:

A 10 m ladder slides down a wall while its foot moves away at 1.5 m/s. When the foot is 6 m from the wall, the top moves down at: