gPoup to complete this worksheet. Return the completed worksheet along th the ho
ID: 2885607 • Letter: G
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gPoup to complete this worksheet. Return the completed worksheet along th the homework exercises at the beginning of next class. All answers must be justified and work shown j l credit. Explanations should be written using complete sentences on the lines provided 1. Below is the graph of the derivative for a function f. Use it to answer the following questions an justify your answers. 12. 4) a) On what interval(s) is f increasing? Decreasing? Find the critical numbers of f. Which critical numbers correspond to local maxima? Loc minima? Neither? b) On what interval(s) is f concave up? Concave down? (Hint you should apply the First Derivative Rule to f"(x):ie. if f"(x) > 0, then f'(x) is increasing) c) d) At what x-value(s) does fhave a point of inflection?Explanation / Answer
The graph is of derivative.
f'(x) = 0 are point of minima or maxima
f''(x) < 0 and f'(x) = 0 is a point of maxima
f''(x) > 0 and f'(x) = 0 is a point of minima
In the interval, where f'(x) > 0 implies function is increasing
In the interval, where f'(x) < 0 implies function is decreasing
(a)
As you can see f'(x) is positive in in (-2,0) U (0,2), so in this interval it is increasing.
f is decreasing in (-3,-2)
(b)
f'(-2) = 0 and f''(x) = (1 - (-1))/(-1 - (-3)) = 2/2 = 1 positive. so x = -2 is a point of maxima
f'(0) = 0 and f''(x) = (1 - 1)/(1 - (-1)) = 0/2 = 0. point of inflection.
No minima
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