2. Let f be differentiable on an open interval I. Use the mean value theorem to show that if
f'(x)>0 for all real x in I, then f increases on I.
1. If is a vector-valued function and let c be a constant. Show that if is differentiable
on come interai I and if =0 for all t ∈ I be I then are orthognal for all t ∈ I .
12.The global minimum value of f(x,y)=2x²+3y²-4x+6 on the region R= is _________
Passage D: Questions 46-50
Logan Herd lost his memory almost completely when he suffered two concussions within minutes of playing baseball. He ended up with retrograde amnesia. He couldn't even remember his parents, his little brother, or his friends and teammates. He was seventeen, and all those memories prior to the night he was injured were completely erased. Dr. Damond Blueitt, Herd's doctor during the injury said that usually, patients with amnesia regain their memory within a year. But that hasn't happened to Herd. Blueitt says the memory loss isn't abnormal but he doesn't know why it's so severe for Herd. Herd still remembered his own name. He could also read and write, but his vocabulary was only at a third-grade level. Herd has had to relearn many things at school. He now knows who Martin Luther King Jr. is, as well as the names of six presidents. Playing baseball came back to Herd naturally though. He still had the fundamentals down, and his first game back gave him so much hope towards his future.
50. What happened to Herd's baseball skills?
(A) He was still able to hit the ball half the time.
(B) He still knew all the essentials of the game.
(C) He had to relearn all the main rules.
(D) He only remembered the coach and nothing else.
49. What happened to Herd's language skills?
(A) He could speak in many languages.
(B) He could read big words but couldn't write them.
(C) He lost many of the words he once knew.
(D) He retained all of them.
48. According to his doctor, what was different about Herd's amnesia?
(A) Herd also acquired some mental side effects.
(B) Herd still hasn't fully regained his memories.
(C) Herd's memory bounced back very quickly.
(D) Herd can still read books very well.