Please Answer These Relative Max and Min Questions - Show Work (#1, 3, 6, 10) 1.
ID: 2831773 • Letter: P
Question
Please Answer These Relative Max and Min Questions - Show Work (#1, 3, 6, 10)
1.
f(x) = -6x2 - 2x - 7
3.
f(x) = 3x4 + 16x3 + 24x2 + 32
A) Relative minimum at (0, 32)
B) Relative minimum at (-2, 48)
C) Relative minimum at (-2, 48), relative maximum at (0, 32)
D) Relative maximum at (-2, 48), relative minimum at (0, 32)
6.
f(x) = 0.2x2 - 2.4x + 5.9
A) Relative minimum at ( 6, -1.3)
B) Relative minimum at ( -6, 27.5)
C) Relative maximum at ( 6, -1.3)
D) Relative minimum at ( 6, 0)
10.
f(x) = -6x3 + 4
A) No relative extrema exist
B) Relative maximum at (0, 4)
C) Relative minimum at (0, 4)
D) Relative maximum at (0, -6)
Explanation / Answer
f(x) = -6x2 - 2x - 7
taking derivative we get f'(x) = -12x - 2 = 0
or x = -1/6
taking the double derivative f''(x) = -12, hence x = 1/6 is the point of maxima
so we get relative maxima at 1/6 with a value of -41/6 i,e, option(C)