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# Extrema

How can you maximize your happiness under a budget? When does a function reach its minimum value? When does a curve change direction? The calculus of extrema explains these "extreme" situations.

You have just started your summer job as a lifeguard at the beach, which has oversized ants leisurely swimming. You are on top of your lifeguard stand and notice that Brilli the ant is making distress signals some distance offshore, and you want to travel to Brilli in the quickest way possible.

Knowing that you travel faster running over sand than you do swimming through water, which of the above best illustrates the quickest path to take?

Assume that the water is still, with no currents.

Is \(f(x)= x + \sin x\) an injective function?

\(AB\) is the ladder and the coordinate of \(R\) is \((8,6)\).

What is the maximumâ€‹ area of a trapezium which has 3 sides of length \( \color{blue} a \)?

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