Differential Calculus: Derivatives & Extrema

A comprehensive 41-page calculus resource focused on derivatives, critical points, local extrema, graph analysis, and parameter problems.
The resource begins with concise review notes covering critical points, extrema, derivative graphs, multiplicity, composite functions, transformations, and graphical interpretation. Students then apply these ideas through structured practice and increasingly challenging parameter problems.
Included
-Key concept review pages
-Critical points and extrema
-Derivative graph analysis
-Composite functions and Chain Rule
-Graphical methods
-Graph transformations
-Double-Graph Method
-Parameter problems
-Practice exercises
-Challenge problems
-Student workspaces
-Detailed worked solutions
Learning Focus
Students practise:
-finding and interpreting critical points;
-identifying local maxima and minima;
-analysing changes in the sign of f′(x)f’(x);
-interpreting graphs;
-counting graph intersections;
-connecting functions with their derivatives;
-solving parameter problems graphically and algebraically;
-applying the Double-Graph Method.
The later questions provide more advanced applications involving parameters, multiplicity, absolute values, and counting extrema.
Suitable For
-High School / Secondary Mathematics
-Calculus
-Differential Calculus
-Derivatives
-Extrema
-Graph Analysis
-Parameter Problems