(a) Choose the correct answer below. (a) The graph in the figure given below is
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Question
(a) Choose the correct answer below. (a) The graph in the figure given below is made of line segments joined end to end. At which points of the interval [-4, 6] is f' not defined? Give reasons for your answer. OA. f' is not defined at x=0, x = 1, and x =4 because at these points the graph has corners. O B. f' is not defined at x = -4, x = 1, and x = 4 because at these points the graph has cusps. O c. f' is not defined at x=0, x= 1, and x = 6 because at these points the graph has cusps. O D. f' is not defined at x = - 4,= 1, and x = 4 because at these points the graph has corners. 7 (0,2) (62) (1.-4) (4.-4) (b) Graph the derivative of f.Explanation / Answer
a) The derivative of the graph will not be defined at all those points where the graph has a sharp edge.
As we can see, the graph has a sharp edge at x=0, x=1 and at x=4 so f' is not defined for these graphs.
Thus, answer is option A
b) For graph of derivative. Calculate the slope of each line segment and plot it;
For (-4,0) to (0,2), slope is = (2-0) / (0-(-4) ) = 2/4 = 1/2
For (0,2) to (1,-4) slope is = (-4-2)/ (1-0) = -6/1 = -6
For (1,-4) to (4,-4) slope is = (-4-(-4) ) / (4-1) = 0/3 =0
For (4,-4) to (6,2) slope is = (2-(-4) ) / (6-4) = 6/2 = 3
Thus, graph of the function will be:
for -4<=x<=0 y= 1/2
for 0<=x<=1 y= -6
for 1<=x<=4 y= 0
for 4<=x<=6 y= 3
The graph will not exist for any other value of 'x'
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