Problem 5: The Mystery of the Derivative
Solve the following calculus problem to test your limits! Let \( f(x) = x^3 - 3x^2 + 5x - 7 \).
Find \( f'(x) \) and determine the critical points. Analyze the intervals of increase and decrease of the function.
- Step 1: Compute the derivative \( f'(x) \) using the power rule.
- Step 2: Set \( f'(x) = 0 \) to find the critical points.
- Step 3: Use the second derivative to test concavity.
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