How Do You Determine Critical Points from a Derivative?

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To determine critical points from the derivative of the function f(x) = x^3 - x^2 + 5, the first step is to find the derivative, which is f'(x) = 3x^2 - 2x. Critical points occur where the derivative is equal to zero or undefined. Setting the derivative equal to zero, 3x^2 - 2x = 0, allows for solving for x, which leads to the critical points. The discussion also prompts users to refer to their textbooks for additional guidance on finding critical points. Understanding these steps is essential for analyzing the function's behavior.
n.a.s.h
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Homework Statement



find the derivative and critical points of the function

f(x)= x^3-x^2+5

Homework Equations





The Attempt at a Solution


I tried to find the derivative: 3x^2-2x but I am not sure how to find the critical points from here...
 
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n.a.s.h said:

Homework Statement



find the derivative and critical points of the function

f(x)= x^3-x^2+5

Homework Equations





The Attempt at a Solution


I tried to find the derivative: 3x^2-2x but I am not sure how to find the critical points from here...
What does your textbook say about finding critical points?
 

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