Solving for c: Finding all Values in (a,b)

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SUMMARY

The discussion focuses on finding all values of c in the open interval (a,b) where the derivative of the function f(x) = (x-2)(x+3)^2 equals zero. The user expresses confusion regarding the relevance of Rolle's Theorem, stating that while it guarantees at least one value in the interval where f' is zero, it does not provide the specific location(s). The solution requires taking the derivative of the function and solving for zero to identify the critical points.

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  • Understanding of calculus concepts, specifically derivatives
  • Familiarity with Rolle's Theorem and its application
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  • Ability to solve equations for critical points
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Homework Statement


Find all values of c in the open interval (a,b) such that f'(x)=0.


Homework Equations


f(x)=(x-2)(x+3)^2 [-3,2]


The Attempt at a Solution

How do I solve this?
 
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I don't see how Rolle's theorem is relevant to solving the problem. All it will tell you is that there is at least one value in the interval where f' is 0. It won't tell you where it(they) is(are). To do that, it seems you simply need to take the derivative, and solve for zero.
 

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