For the following function, find the relative max's or min's using any method.
I'm having a hard time finding the critical points...
Sorry, I forgot to post the function:
f(x)=cos3x
surely you jest! The critical points are where f' = 0.
f'(x) = -3sin3x
You know that sin(u)=0 when u is a multiple of pi.
So, f'(x) = 0 when 3x is a multiple of pi:
x= 0, pi/3, 2pi/3, ...
To find the relative maxima and minima of a function, you need to first identify the critical points. Critical points occur where the derivative of the function is either zero or undefined.
Here's a step-by-step guide to finding the critical points:
1. Start by finding the derivative of the function.
- If your function is f(x), then find f'(x), which represents the derivative of f(x).
- The derivative is used to determine the rate at which the function is changing.
2. Set the derivative f'(x) equal to zero and solve for x.
- This step helps you find the x-values where the function is neither increasing nor decreasing (i.e., where the slope is zero).
- Set f'(x) = 0 and solve the equation to find the x-values.
3. Check for points where the derivative is undefined.
- At these points, the function may have a relative extremum (maximum or minimum).
4. Evaluate the function at each critical point and the points where the derivative is undefined.
- Substitute the x-values into the original function to find the corresponding y-values.
5. Determine the nature of each critical point.
- Use the second derivative test or the first derivative test to identify whether each point is a relative maximum or minimum.
The critical points and their corresponding nature will help you identify the relative maxima and minima of the function.
If you provide the specific function, I can help you find the critical points and determine the relative maxima and minima.