Increasing Function: Finding k When x=pi/4

In summary, when x=pi/4, the rate at which sinx^2 is increasing is k times the rate at which x is increasing. The value of k is 1. To find the rate at which x is increasing, you can simply take the slope of sinx^2 when x=pi/4, which is also 1.
  • #1
coookiemonste
24
0

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 don't know how to find the rate at which x is increasing.
do i just take an average slope?
 
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  • #2
Hint: (dy/dt) / (dx/dt) = dy/dx.
 
  • #3
i think dy/dt would be 1.
how do i find dx/dt?
 
  • #4
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
Yes, that's right. :smile:
 

FAQ: Increasing Function: Finding k When x=pi/4

What is the purpose of finding k when x=pi/4 in increasing function?

The purpose of finding k when x=pi/4 in increasing function is to determine the rate at which the function is increasing at a specific point. This allows us to better understand the behavior of the function and make predictions about its values at other points.

How do you find the value of k when x=pi/4 in an increasing function?

To find the value of k when x=pi/4 in an increasing function, we can use the slope formula: k = (f(pi/4 + h) - f(pi/4)) / h. We can also use the derivative of the function and plug in x=pi/4 to solve for k.

Why is it important to know the value of k when x=pi/4 in an increasing function?

Knowing the value of k when x=pi/4 in an increasing function allows us to calculate the slope of the function at that point, which gives us information about its behavior. This is important in understanding the overall behavior of the function and making predictions about its values at other points.

Can you find the value of k for any function when x=pi/4?

Yes, the value of k when x=pi/4 can be found for any function as long as the function is continuous and differentiable at x=pi/4. This means that the function must have a well-defined slope at that point in order to find the value of k.

How does finding k when x=pi/4 relate to the concept of increasing functions?

Finding k when x=pi/4 is directly related to the concept of increasing functions because it allows us to determine the rate at which the function is increasing at that specific point. This information is essential in understanding the behavior of increasing functions and making predictions about their values at other points.

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