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Posted on 2014-11-19

f ( theta ) = 2 sec ( theta ) + tan ( theta )

0 <= theta < 2 pi

f ' ( theta ) = sec ( theta ) * [ 2 tan ( theta ) + sec ( theta ) ]

set derivative to 0 to find critical numbers.

sec ( theta ) * [ 2 tan ( theta ) + sec ( theta ) ] = 0

The only way I know how to do this problem is to plug different angle values for theta. The values that

satisfy the equation are critical numbers.

Is there a better way to do this problem ? Is there a method or procedure ?

This problem is from Advanced Placement High School Calculus class.

0 <= theta < 2 pi

f ' ( theta ) = sec ( theta ) * [ 2 tan ( theta ) + sec ( theta ) ]

set derivative to 0 to find critical numbers.

sec ( theta ) * [ 2 tan ( theta ) + sec ( theta ) ] = 0

The only way I know how to do this problem is to plug different angle values for theta. The values that

satisfy the equation are critical numbers.

Is there a better way to do this problem ? Is there a method or procedure ?

This problem is from Advanced Placement High School Calculus class.

2 Comments

which means 2 sin ( theta ) + 1 = 0

If you want to solve it numerically rather than analytically, and you plug different angle values for theta such that

2 sin ( theta1 ) + 1 > 0 and 2 sin ( theta2 ) + 1 < 0 then you know that 2 sin ( theta ) + 1 = 0 for some theta between theta1 and theta2, and you can binary search to narrow it down

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