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.
