MA113_S13_Assignment4_solutions

# MA113_S13_Assignment4_solutions - MA 113 Calculus I Spring...

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MA 113 – Calculus I – Spring 2013 Written Assignment #4 Due Friday, March 1, 2013, at beginning of lecture Question A: Figure (A) shows f and figure (B) shows f ′′ . Sketch the graph of f and explain your reasoning. 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 (A) (B) Solution: We can see by looking at figure (A) that the graph of f has a horizontal tangent line at x = - 1 and x = - 0 . 25. Then the graph of f will have x -intercepts at x = - 1 and x = - 0 . 25. We also note that f ( x ) is decreasing when x is in interval ( - 1 , - 0 . 25) and f ( x ) is increasing for x in the intervals ( -∞ , - 1) and ( - 0 . 25 , ). Hench the graph of f will be negative for x in the interval ( - 1 , - 0 . 25) and positive when x is in the intervals ( -∞ , - 1) and ( - 0 . 25 , ). Next we examine figure (B). From the graph we see that f ′′ ( - 2 / 3) = 0, thus the derivative of f ( x ) is 0 at x = - 2 / 3. In other words, the graph of f has one horizontal tangent line at x = - 2 / 3.

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