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How many ciritcal points functionf(x)=(x...

How many ciritcal points functionf(x)=(x-1)|x-3|-4x+12 has? How many of these are points of local extrema?

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To solve the problem, we need to analyze the function \( f(x) = (x - 1)|x - 3| - 4x + 12 \) to find its critical points and determine how many of these points are local extrema. ### Step 1: Identify the piecewise nature of the function The function contains an absolute value, \( |x - 3| \), which means we need to consider two cases based on the value of \( x \): 1. **Case 1**: \( x < 3 \) - Here, \( |x - 3| = 3 - x \). - Therefore, the function becomes: ...
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