Rex Reed, the film critic and author whose pithy reviews and provocative Hollywood interviews established him as a bad boy of entertainment journalism, died Tuesday morning, his rep told The Hollywood Reporter . He was 87. Reed died at his home in Manhattan after a short illness, according to friend William Kapfer, the rep said. He lived since 1970 in a New York apartment in the Dakota that he bought for $30,000. The Louisianian penned film reviews and columns for the  New York Observer  since the newspaper’s start in 1987 (he was laid off for a spell in 2017 before being rehired), and his final review was for the film Truth & Treason in November. Earlier, he spent 13 years as an arts critic for the  New York Daily News  and five with the  New York Post . Reed was not the typical dowdy or frumpy critic.…