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Sketch the function and find local maximum and local minimum- Maths- Calculus

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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.

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									              Sub: Mathematics                                                                              Topic: Calculus



              Question:

              Find whether x=3 is a local maximum or a local minimum and Sketch the graph
              for all cases.
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              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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