Sketching the derivative of a function

Task goals

• Locate stationary points of f and transfer their x-values to zeros of f'.
• Use increasing and decreasing intervals of f to determine the sign of f'.
• Use relative tangent steepness to estimate the magnitude of f'.
• Use concavity of f to determine whether f' is increasing or decreasing.
• Distinguish a crossing derivative zero from a touching derivative zero.
• Sketch linear, quadratic, and cubic derivative graphs from polynomial function graphs.
• Explain why vertical translations of a function have the same derivative.
• Identify contradictions between a proposed derivative and the supplied function.
• Optionally verify a derivative sketch by differentiating exactly.