2. Let g: RR be a measurable function such that fx|g|dm <∞ (here m is the Lebesgue measure). Show that lim n→+∞ (*_ \9(x)|dx + [_~_* 19(x)\dx) = 0. n

If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local extremum offon (a,c) ?

Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.

3. Let f(x) = 8x- 3x*+5 %3! a) Find where f has stationary points. b) Perform a sign analysis on the derivative of f. Find where f is increasing and decreasing. c) Use your results to find where all local maxima and minima of foccur.