Does the function exist?

Calculus Level 2

f ( x ) f ′ ( x ) = tan ⁡ ( x ) \large \cfrac{f(x)}{f'(x)}=\tan(x)

How many functions, if any, satisfy this?

If there are infinitely many, use -1 as your input.


The answer is -1.

James Watson by James Watson , 16, United Kingdom

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1 solution

Solution to the given equation is f ( x ) = C sin ⁡ x f(x)=C\sin x , where C C is the integration constant. Since C C can assume infinitely many values, there are infinite number of solutions. Hence the answer is − 1 + 3 = 2 -1+3=\boxed 2 .

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The correct answer is now − 1 -1 , by the same method. The question has been updated to remove the requirement to answer A + 3 A+3 instead of A A .

Matthew Christopher - 10 months, 2 weeks ago

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