f'(x)=0
When the derivative f'(x) is equal to 0, it means that the rate of change of the function f(x) at that particular point is zero
When the derivative f'(x) is equal to 0, it means that the rate of change of the function f(x) at that particular point is zero. In other words, the slope of the tangent line to the graph of f(x) at that point is horizontal or flat.
To find the x-values where f'(x) = 0, you need to solve the equation f'(x) = 0. This can be done by finding the critical points, which are the points where the derivative is either 0 or undefined.
Here’s an example to illustrate the process:
Let’s say we have the function f(x) = x^2 – 4x + 3. To find the critical points, we first need to find the derivative f'(x) of the function:
f'(x) = 2x – 4
Now, set f'(x) = 0 and solve for x:
2x – 4 = 0
2x = 4
x = 2
So, the critical point is x = 2, where the derivative f'(x) is equal to 0.
In summary, when f'(x) = 0, it indicates that the function has a critical point where the rate of change is zero. Finding the x-values where f'(x) = 0 can help determine important information about the behavior of the function such as maximum or minimum points.
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