Unit 1
If f(t) = 3t2 - 10t + 2, will f(x) = 1 on the interval [-1, 3]?
yes. f(-1) = 15 and f(3) = -1
Another name for a derivative?
Slope/rate of change
To find the velocity function from the position function
Derivative
When f'(x) > 0, f(x) is
increasing
The equation of the tangent line through the point (-1, -2), if dy/dx = 1 - xy
y + 2 = -1(x+1)
The domain of f(x) = x2 - x / x
All real numbers, except zero
What is the derivative of f(x) = 8x2 - 6
16x
The acceleration function if x(t) = t3 - 4t2 + 3
x"(t) = a(t) = 6t - 8
If f"(x) < 0, f(x) is
concave down
y = 5e6t
The limit as x approaches 1 for (x2-5x)/(x - 1)
Does not exist.
The derivative of f(x) = (x2 - 5)4
8x(x2 - 5)3
v(t) and a(t) have the same sign
The linear motion of an object when f'(x) changes signs
The object changes direction
The average value of f(x) = 6 - x2 on [-1, 3]
11/3
The limit as x approaches 8 for (x2 + 2x - 80) / x- 8
18
The derivative of f(x) = 3x - 4cosx
3xln3 + 4sinx
Given the position s(t) = 1/3t3 - 3t2 + 8t - 5, the particle is at rest when t =
t = 4 and t = 2
The value of the integral of (4 - 6x) dx from -2 to 5
-35
The formula to find the volume of a solid with semicircles cross sections
V = integral a to b of 1/2 pi r^2 dx where r is f(x) - g(x) / 2
The limit as x approaches 2 for (x2 + 6x - 16) / 2 - x
-10
The simplified derivative of h(x) = (3x + 1) / 2x2
-3x - 2 / 2x3
What law is used when a limit equals 0/0?
L'Hopital's Rule
The indefinite integral of 6x2(x3 + 4)5 dx
1/3(x3 + 4)6 + C
The volume bounded by y = 4 - 2x, y = 0, and x = 0. Revolved about the y-axis.
16pi/3