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How to prove that 1 is the max value of cos(cosx) through APPLICATION OF DERIVATIVES.

How to prove that 1 is the max value of cos(cosx) through APPLICATION OF DERIVATIVES.

Grade:12

1 Answers

Himanshu
389 Points
5 years ago
let f(X)=cos(cosx)
then derivative of f(x) is -sin(cosx)*-sinx= sin(cosx)*sinx
for maxima or minima derivative =0
hence sinx=0 or sin(cosx)=0
calculate the values of x
now double derivative is cos(cosx)*-sinx*sinx+sin(cosx)*cosx
putting values obtained in step 2 check for which values of x double derivative is negative
put these values in original functions this is the maximum valyue

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