2 Let f be twice differentiable on R and suppose f x 0 for

Last updated: 10/24/2023

2 Let f be twice differentiable on R and suppose f x 0 for all x ER a Show that f is monotonic on R i e that f is increasing on all of R or decreasing on all of R b Show that f is increasing if and only if f 1 is increasing Note To show this if and only if you must show two implications if f is increasing then f is increasing and if f 1 is increasing then f is increasing c Show that if f is increasing and concave up everywhere then f 1 is increasing and concave down everywhere