Identify the important points (critical number and endpoints) needed to find the
ID: 2882640 • Letter: I
Question
Identify the important points (critical number and endpoints) needed to find the maximum and minimum value on the
given closed interval I.
8) r() = 2 cos ; I = [- /4, /3]
A) Important points: - /4, 2, /3; maximum value sqrt(2); minimum value 1
B) Important points: 0; maximum value 2; no minimum value
C) Important points: - /4, 0, /3; maximum value 2; minimum value 1
D) Important points: - /4, 0, /3; maximum value 2; minimum value sqrt(2)
9) g(t) = t^2/3; I = [-1, 8]
A) Important points: -1, 0, 8; maximum value 1; minimum value 0
B) Important points: -1, 8; maximum value 4; minimum value 3
C) Important points: 0; no maximum value; minimum value 0
D) Important points: -1, 0, 8; maximum value 4; minimum value 0
Explanation / Answer
8) A
as cos varies from 1/sqrt(2) to 0.5 in the interval [- /4, /3]
that imples maximum value of 2cos = 2*1/sqrt(2) = sqrt(2)
and the minimum value = 2*0.5 = 1
9) D
g(t) = t^2/3 I = [-1, 8]
at 8 g(t) = maximum = 4
and at 0 g(t) = minimum = 0