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QA: (inspired by a problem from Stewart’s textbook) Suppose that there is some function f whose...

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Basic Math

QA: (inspired by a problem from Stewart’s textbook) Suppose thatthere is some function f whose _derivative_ is f ’ =sin(x)/x, withf ‘(0)=1 by definition rather than DNE. Draw that, on the interval[-4pi,+4pi].

(i) On what intervals is the original f increasing? Decreasing?Indicate the intervals on the graph as well as writing them ininterval notation like [0,pi]

(ii) At what x values does f have a local max? A local min?Indicate them on the graph as well as writing them out like: maxesat …. ; mins at ….

(iii) On what intervals is f CD? CU? Indicate the intervals onthe graph as well as writing them in interval notation.

(iv) At what x values does f have an inflection point? Indicatethem on the graph as well as writing them out like: IP at ...

(v) Sketch a graph of f, starting at f(0)=0.

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