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Increasing function

  • #1

Homework Statement


When x=pi/4, the rate at which sinx^2 is increasing is k times the rate at which x is increasing. What is the value of k?
(answer is 1)


Homework Equations





The Attempt at a Solution


I plugged in pi/4 into sinx^2 and i got .5.
i also took the derivative of sinx^2 and plugged in pi/4 to get the slope, which is 1.
So it seems to me that I found the rate at which sinx^2 is increasing (1), but i dont know how to find the rate at which x is increasing.
do i just take an average slope?
 

Answers and Replies

  • #2
dx
Homework Helper
Gold Member
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18
Hint: (dy/dt) / (dx/dt) = dy/dx.
 
  • #3
i think dy/dt would be 1.
how do i find dx/dt?
 
  • #4
dx
Homework Helper
Gold Member
2,011
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dx/dt is not given and is not needed. You only know that the ratio dy/dt and dx/dt is k. But the ratio of dy/dt and dx/dt is dy/dx, so what does that tell you?
 
  • #5
that it is just simply the slope of sinx^2 when x=pi/4
which is 1
?
 
  • #6
dx
Homework Helper
Gold Member
2,011
18
Yes, that's right. :smile:
 

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