Stage: 5 Challenge Level: 
Draw a sketch of the graph of $f(x)$ for $a\leq x \leq b$ and
interpret from your diagram $bf(b) - af(a).$
Discussion. Turning points. Maths in STEM. Functions and their inverses. physics. Asymptotes. Graph sketching. Symmetry. Families of Graphs. Integration.
Published September 2004,July 2009,August 2009.
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