question_answer 21)

Find the intervals in which f(x) = 2x3 – 3x2 – 36x + 7 is (a) strictly increasing (b) strictly decreasin+  

Answer:

f(x) = 2x3 ? 3x2 ? 36x + 7                  f?(x) = 6x2 ? 6x ? 36       = 6(x2 ? x ? 6)       = 6 (x ? 3) (x + 2)       f?(x) = 0 x = ?2, 3       Intervals are :       when  then f?(x) = 6 (?)(?) > 0       when  then f?(x) = 6 (?)(+) < 0       when  then f?(x) = 6 (+)(+) > 0 (a)   f(x) is strictly increasing in (b)   f(x) is strictly decreasing in (?2, 3).