In the xy-plane, the graph of the parametric equations x = 5t + 2 and y = 3t, for –3 ( t ( 3, is a line segment with slope
3/5
2
3
5/3
1/3
1/2
3/8
1
3/4
Non-existent
The slope of the line tangent to the curve
y2 + (xy + 1)3 = 0 at (2, –1) is
3/4
-3/4
-2/3
1
-3/2
If ƒ and g are twice differentiable and if h(x) = ƒ(g(x)), then h”(x) =
ƒ"(g(x))g’(x) + ƒ’(g(x))g”(x)
ƒ"(g(x))
ƒ"(g(x))g’’(x)
ƒ"(g(x))[g”(x)]2
ƒ”(g(x))[g’(x)]2 + ƒ’(g(x))g”(x)
A particle moves on a plane curve so that at any time t > 0 its x-coordinate is t3 – t and its y-coordinate is (2t – 1)3. The acceleration vector of the particle at t = 1 is
(0, 1)
(2, 4)
(2, 8)
(6, 24)
(6, 12)
If ƒ is the function defined by ƒ(x) = 3x5 – 5x4, what are all the x-coordinates of points of inflection for the graph of ƒ?
–1
1
0 and 1
0 only
–1, 0 and 1
The acceleration of a particle moving along the x-axis at time t is given by a (t) = 4t + 1. If the velocity is 15 when t = 3 and the position is 10 when t = 6, then the position x(t) =
ƒ"(1) < ƒ(1) < ƒ’(1)
ƒ(1) < ƒ”(1) < ƒ’(1)
ƒ(1) < ƒ’(1) < ƒ”(1)
ƒ'(1) < ƒ(1) < ƒ”(1)
ƒ"(1) < ƒ’(1) < ƒ(1)
4
-4
1
-2
3
For what value of x does the function
f(x) = (x +3)3(x –1)2 have relative minimum?
–3
-3/5
-5/2
1/3
1
0
-1/2
1/2
-3/5
Non-existent
6.08 only
7.8 only
7.8 and 9.2
6.08 and 17.9
5
5
0
1
2
6
-1
increasing for x < –10, decreasing for –10 < x< 2, increasing for x > 2
decreasing for x < 2, increasing for x > 2
increasing for all x
decreasing for all x
decreasing for x < –10, increasing for –10 < x < 2, decreasing for x > 2
How many critical points does the function
f(x) = (x -5)3(x+2)2 have?
Nine
Five
One
Two
Three
10/3
8/3
40/3
20/3
15
1
-1/4
-2/3
1/4
-1