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Questions
MAT-265-OD24-02-7799
Multiple fill-in-the-blank
Maxima and Minima Graph the function Find the value of at which the given has a local maximum. Round to the nearest hundredth. [Fill in the blank] Find the value of at which the given has a local minimum. Round to the nearest hundredth. [Fill in the blank]

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Standard Answer
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Approach Analysis
We start by identifying the critical points of the function to locate potential local maxima and minima.
Option set: The problem asks for the x-values where the given f(x) = x^3 - 4x^2 - 3x + 1 has a local maximum and a local minimum. The derivative will guide us to candidate points.
1) Compute the derivative: f'(x) = d/dx [x^3 - 4x^2 - 3x + 1] = 3x^2 - 8x - 3.
2) Find critical points by solving f'(x) = 0:
3x^2 - 8x - 3 = 0.
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