If ƒ(x) = ln(sin4 x+ 1), then ƒ’(x) =
The average value of cos2x on the interval [–2, 2] is
0
1/e
1
e
Non-existent
1
-18cos6x
-2cos6x
2cos6x
18cos6x
2sin3xcosx
If f(x) = x3 + 3x2 +4x +5 and g(x) = 5, then g’(f(x)) =
1125
0
5
If f(x) =x +sinx, then f’’(x) =
- sinx
1 – cosx
Cos x
1-sinx
Sin x +cos x
-1
-1/2
0
½
1
1/3
7/3
3
7
8
-1
0
1
4/3
5/3
The area of the region bounded by the lines x = 0, x = 3, and y = 0 and the curve y = ex/3 is
e-1
3( e-1)
3e-1
3e
3/2
337/3
343/6
31/6
335/2
2
3
6
11
13
sinx
1
cosx
If a function is continuous for all x and if f has a relative maximum at (-2, 3) and a relative minimum at (5, -3) which of the following statements must be true?
The graph of f has a point of inflection somewhere between x = -3 and x =3
f’(-1)=0
The graph of f has a horizontal asymptote
The graph of f has a horizontal tangent line at x = 3
The graph of f intersects both the axes.
-3/4
7/2
-8
16
0
1/e
1
2e
Sec2e
The area of the region enclosed by the graph of
y = x2 + 4 and the line y = 8 is
14/3
16/3
28/3
32/3
8(