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1 Apr 2020
The figure shows the graph of the derivative
of a function f.
(a) On what intervals is f increasing or decreasing?
(b) For what values of x does f have a local maximum or minimum?
(c) Sketch the graph of
.
(d) Sketch a possible graph of f.
![](data:image/png;base64,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)
The figure shows the graph of the derivative of a function f.
(a) On what intervals is f increasing or decreasing?
(b) For what values of x does f have a local maximum or minimum?
(c) Sketch the graph of .
(d) Sketch a possible graph of f.
Keith LeannonLv2
29 May 2020