E-GR04 · Read the graph, then count intersections
The diagram shows \(y=a+b\cos(kx)\), where \(b,k\gt 0\), on \(0\le x\lt \pi\). Consecutive maxima are \((0,7)\) and \(\displaystyle (\frac{\pi }{2}, 7)\), with minimum \(\displaystyle (\frac{\pi }{4}, - 1)\) between them.
Find \(a,b,k\).
Now restrict the domain to \(\displaystyle 0\le x\le \frac{\pi }{8}\). Find its range.
Return to \(0\le x\lt \pi\). Find all real \(h\) for which \(a+b\cos(kx)=h\) has exactly four distinct solutions. Explain the boundary cases.
Complete-answer checking, worked solutions and indicative written criteria.
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