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What is the number of critical points of f(x)=max(sinx,cosx) in the intervasl (-2π,2π)?

What is the number of critical points of f(x)=max(sinx,cosx) in  the intervasl (-2π,2π)?

Grade:10

1 Answers

Ajay
209 Points
4 years ago
First you need to draw graph for max (sinx, cosx ) as follows
Draw combined graphs of both sinx and cos x so that at some places graph of sin x will be higher and at other cosx will higher.
Take only the higher portion of graph and mark it bold. This will give you the graph of  f(x)=max(sinx,cosx).
Critical points are points on graph where the derivative is 0 or undefined.
Now you can easily check the points which are high or low (critical points). The number of such points comes out to be 7

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