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Questions
Questions

MAT-265-OD24-02-7799 Prior Knowledge Check

Multiple fill-in-the-blank

Maxima and Minima Graph the function f(x)=x3−4x2−3x+1f\left(x\right)=x^3-4x^2-3x+1 Find the value of xx at which the given f(x)f\left(x\right) has a local maximum. Round to the nearest hundredth. [Fill in the blank] Find the value of xx at which the given f(x)f\left(x\right) has a local minimum. Round to the nearest hundredth. [Fill in the blank]

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Approach Analysis
We start by finding where the derivative is zero to locate potential local extrema. 1) Compute f'(x) for f(x) = x^3 - 4x^2 - 3x + 1: f'(x) = 3x^2 - 8x - 3. 2) Solve f'(x) = 0: 3x^2 - 8x - 3 = 0. Discriminant D = (-8)^2 - 4(3)(-3) = 64 ......Login to view full explanation

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