Directions: Fill in the boxes below using the digits 1 to 6, at most one time each, to make the largest value for D (the derivative).

### Hint

What values give an output of 1 or 1/2 to the derivative of sin(x)?

### Answer

sin^6(x) and f'(4pi/2)…or sin^6(x) and f'(2pi/1)

Source: Chris Luzniak

I don’t think your answer is correct.

The derivative of f(x)=sin^6(x) is f'(x)=6sin^5(x)*cos(x)

So f'(2pi)=0 b/c sin(2pi)=0

I believe the correct answer should be f(x)=sin^6(x) and f'(1pi/3)=1.461

I agree, maximizing cosine will zero the sine function. Mr. H has the correct answer, to the best of my ability to judge.

Thanks Chris and Mr. H

I believe that f'(4pi/3) = f'(pi/3) so this provides another possible solution.

Yes, I believe that you are correct Mr. H.