The graph of f', the derivative of the function f, is shown above. Which of the following could be the graph of f?
1 answer:
In the region 0-2, the first derivative has a zero at x=1, and the second derivative (slope of the first derivative line) is positive. This means f(x) will have a minimum at x=1.
Likewise, in the region 4-6, the second derivative is negative and the first derivative is zero at x=5, indicating a maximum there.
These observations narrow the selection to choices A or C. The derivative curve is continuous at x=2 and x=4, so there will not be any discontinuities in f(x)--eliminating selection C.
The best choice is A.
Likewise, in the region 4-6, the second derivative is negative and the first derivative is zero at x=5, indicating a maximum there.
These observations narrow the selection to choices A or C. The derivative curve is continuous at x=2 and x=4, so there will not be any discontinuities in f(x)--eliminating selection C.
The best choice is A.
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