Let f(x) be a continuous function which satisfies the following conditions.
f(0) = 4; f(2) = 2; f(5) = 6 f?'(0) = f?'(2) = 0
f?'(x) > 0 if |x ? 1| > 1
f?'(x) < 0 if |x ? 1| < 1
f?''(x) < 0 if x < 1 or if |x ? 4| < 1
f?''(x) > 0 if |x ? 2| < 1 or if x > 5
a)Find the intervals on which f is increasing. (Enter your answer as a comma-separated list of intervals.)
b)Find the intervals on which f is decreasing. (Enter your answer as a comma-separated list of intervals.)
c)Find the largest open intervals on which f is concave up. (Enter your answer as a comma-separated list of intervals.)
d)Find the largest open intervals on which f is concave down. (Enter your answer as a comma-separated list of intervals.)
e)Identify all local maxima and minima. (Enter your answers as comma-separated lists.)
Local Min?
Local Max?