Analyze f(x)=[ex]/(x-1) on the closed interval [0,3] without using your graphing calculator. When done, you can verify your results on a graphing calculator.
Find local/global extrema, and sketch f(x). What about inflection
points? What are the local/absolute extrema on [1.5,3]?
Using the quotient rule,
f'(x)=
Using the Quotient Rule and several simplifications, f''(x)=
Intervals where f is increasing:
Intervals where f is decreasing:
Intervals where f is concave up:
Intervals where f is concave down:
Local Max:
Local Min:
Absolute Max:
Absolute Min:
What about points of inflection?
Your sketch:
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