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Sketching the graph using local max and local min: Find whether x = 3 is a local maximum or a local minimum and sketch the graph for all cases.
Sub: Mathematics Topic: Calculus Question: Find whether x=3 is a local maximum or a local minimum and Sketch the graph for all cases. ClassOf1 provides expert guidance to College, Graduate, and High school students on homework and assignment problems in Math, Sciences, Finance, Marketing, Statistics, Economics, Engineering, and many other subjects. The function f has a derivative everywhere and has just one critical point, at x=3. In parts (a) to (d), you are given additional conditions. In each case decide whether x=3 is a local maximum, a local minimum, or neither. Explain your reasoning. Sketch possible graphs for all four cases. (a) f ’(1) = 3 and f ’(5) = -1 (b) f (x) → ∞ as x → ∞ and as x → - ∞ (c) f (1) = 1, f (2), f (4) = 4, f (5) =5 (d) f ’(2) = -1, f (3) =1, f (x) → 3 as x→ ∞ Solution:
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